At 32 years old, Saudi Arabia's Crown Prince Mohammed bin Salman is already the most dominant Arab leader in a generation. This week, he embarks on a cross-country American tour, where he'll pitch his kingdom to a skeptical U.S. public. He was named heir to the throne nine months ago by his 82-year-old father, King Salman, who granted his son vast new powers.

Known by his initials -- "M-B-S" -- his reforms inside Saudi Arabia have been revolutionary. He is emancipating women, introducing music and cinema and cracking down on corruption, in a land with 15,000 princes. But selling Saudi Arabia won't be easy. In his first interview with an American television network, he was eager to discuss his country's promise and its troubled reputation head-on.

Norah O'Donnell: When many Americans think about Saudi Arabia, they think about Osama bin Laden and 9/11. They think about the terrorism that he brought to American soil.

Mohammed bin Salman: Right. Osama bin Laden recruited 15 Saudis in the 9/11 attacks with a clear objective. According to the CIA documents and Congressional investigations, Osama bin Laden wanted to create a schism between the Middle East and the West, between Saudi Arabia and the United States of America.

Saudi Arabia's Crown Prince Mohammed bin Salman CBS News

Norah O'Donnell: Why did Osama bin Laden wanna create that hatred between the West and Saudi Arabia?

Mohammed bin Salman: In order to create an environment conducive to recruitment and spreading his radical message that the west is plotting to destroy you. Indeed he succeeded in creating this schism in the west.

Norah O'Donnell: And how do you change that? Because it looks like what you're trying to do is change things here at home.

Mohammed bin Salman: Indeed. I believe that we have succeeded in many respects in the last three years.

We first met Prince Mohammed at the Royal Court in Riyadh. He arrived in a driving rain, a sign of good fortune in the desert kingdom. He's been called bold and visionary for his reforms at home, as well as reckless and impulsive in his rise to power. He has kicked a hornet's nest in the Middle East and earned a host of new enemies, partly why he's one of the most heavily-guarded men in the world. This is the office where he starts his days.

Norah O'Donnell: Working hard?

Mohammed bin Salman in English: Always.

He learned English from watching movies as a kid. And he's acutely aware that 70 percent of the population is like him, under the age of 35 – and getting restless.

Norah O'Donnell: What's been the biggest challenge?

Mohammed bin Salman in English: There's a lot of challenge. I think the first big challenge that we have is do the people believe in what we are doing.

Norah O'Donnell: There is a widespread perception that the kind of Islam practiced inside Arabia is harsh, it's strict, it's intolerant. Is there any truth to that?

Mohammed bin Salman: After 1979, that's true. We were victims, especially my generation that suffered from this a great deal.

The crown prince traces most of Saudi Arabia's problems to the year 1979, when the Ayatollah Khomeini established an Islamic theocracy next door in Iran. The same year, religious extremists in Saudi Arabia took over Islam's holiest site, the Grand Mosque in Mecca. In order to appease their own religious radicals, the Saudis began clamping down and segregating women from everyday life.

Norah O'Donnell: What has been this Saudi Arabia for the past 40 years? Is that the real Saudi Arabia?

Mohammed bin Salman: Absolutely not. This is not the real Saudi Arabia. I would ask your viewers to use their smartphones to find out. And they can google Saudi Arabia in the 70s and 60s, and they will see the real Saudi Arabia easily in the pictures.

Norah O'Donnell: What was Saudi Arabia like before 1979?

Mohammed bin Salman: We were living a very normal life like the rest of the Gulf countries. Women were driving cars. There were movie theaters in Saudi Arabia. Women worked everywhere. We were just normal people developing like any other country in the world until the events of 1979.

Saudi women -- who've been virtually invisible in public -- have been given new rights, making it easier for them to start a business, join the military, and attend concerts and sporting events. In June, they will be able to get behind the wheel and drive.

Norah O'Donnell: Are women equal to men?

Mohammed bin Salman: Absolutely. We are all human beings and there is no difference.

Norah O'Donnell: You have said you are, "Taking Saudi Arabia back to what we were, a moderate Islam." What does that mean?

Mohammed bin Salman: We have extremists who forbid mixing between the two sexes and are unable to differentiate between a man and a woman alone together and their being together in a workplace. Many of those ideas contradict the way of life during the time of the prophet and the Caliphs. This is the real example and the true model.

He has curbed the powers of the country's so-called "religious police," who until recently were able to arrest women for not covering up. And listen carefully to what he says is not part of Islamic Law.

Mohammed bin Salman: The laws are very clear and stipulated in the laws of Sharia: that women wear decent, respectful clothing, like men. This, however, does not particularly specify a black abaya or a black head cover. The decision is entirely left for women to decide what type of decent and respectful attire she chooses to wear.

His words are significant, and so far, the kingdom's religious leaders are holding their tongues, and have sworn allegiance to the young prince.

Saudi Arabia's Crown Prince Mohammed bin Salman CBS News

Of all of the meetings he presides over every week, this is the most important: his economic council. These are the men, and a few women, trusted with re-making Saudi Arabia's "social pact" with its people. One of the crown prince's closest advisers is Mohammed al-Sheikh, a Saudi-born, Harvard-trained lawyer.

Mohammed al-Sheikh: We had a young population. And we were providing for the population, you know subsidized energy, subsidized water, subsidized medicine, subsidized education, we subsidized everybody's life.

Norah O'Donnell: And no taxes.

Mohammed al-Sheikh: And no taxes.

Norah O'Donnell: How close was Saudi Arabia to a financial crisis?

Mohammed al-Sheikh: I don't think it was extremely close, but it was heading in that direction.

Reforming the welfare state is one challenge. Another is what the crown prince calls Saudi Arabia's "addiction" to oil. The state oil company, Aramco, is valued at $2 trillion. Under the crown prince's plan, some of it will be sold off to invest in new ventures. There are concerns that the kingdom's secretive finances and dismal record on human rights may spook investors.

Norah O'Donnell: You have promised transparency and openness. But there are reports that dozens of people who have criticized your government have been arrested in the last year. They include economists, clerics, intellectuals. Is this really an open and free society?

Mohammed bin Salman: We will try to publicize as much as we can and as fast as we can, information about these individuals in order to make the world aware of what the government of Saudi Arabia is doing to combat radicalism.

Norah O'Donnell: But to answer the question about human rights abuses in this country.

Mohammed bin Salman: Saudi Arabia believes in many of the principles of human rights. In fact, we believe in the notion of human rights, but ultimately Saudi standards are not the same as American standards. I don't want to say that we don't have shortcomings. We certainly do. But naturally, we are working to mend these shortcomings.

But the crown prince has been accused of heavy-handed tactics. The most extraordinary example happened last November, at the Ritz-Carlton Hotel in Riyadh. He invited hundreds of current and former government ministers, media moguls, prominent businessmen, and at least 11 princes to a meeting here, where they were accused of stealing from the state and were held until they either paid it back or proved their innocence.

Norah O'Donnell: I mean, what happened at the Ritz-Carlton? How did that work? You were, essentially, the Ritz-Carlton became a jail.

Mohammed bin Salman: What we did in Saudi Arabia was extremely necessary. All actions taken were in accordance with existing and published laws.

Among the detained was Prince Alwaleed bin Talal -- one of the richest men in the world. After Prince Alwaleed was detained for more than two months, the Saudis allowed a camera crew inside his room at the Ritz for a brief interview.

Prince Alwaleed: And I'd like to stay here until this thing's over completely and get out and life goes on.

Mohammed al-Sheikh said the crackdown was necessary.

Mohammed al-Sheikh: It wasn't easy. Just given the names and given the people who were involved, it really wasn't easy. But we-- we just felt that we had to do this. And and we had to do it that way.

Norah O'Donnell: What kinda corruption are we talking about? I mean, how much money was disappearing?

Mohammed al-Sheikh: Probably 5 to 10 percent of the annual spend by the government, which was roughly, I would say anywhere between $10-20 billion, maybe even more, on an annual basis.

Norah O'Donnell: So $20 billion a year is just disappearing?

Mohammed al-Sheikh: Disappearing.

There have been reports that some detainees were physically abused, and one died in custody. The Saudis told us the choice of the hotel, "was to maintain the respect, dignity and… comfort for those being investigated."

Norah O'Donnell: Was it a power grab?

Mohammed bin Salman: If I have the power and the king has the power to take action against influential people, then you are already fundamentally strong. These are naïve accusations.

Norah O'Donnell: How much money did you get back?

Mohammed bin Salman: The amount exceeds $100 billion, but the real objective was not this amount or any other amount. The idea is not to get money, but to punish the corrupt and send a clear signal that whoever engages in corrupt deals will face the law.

Norah O'Donnell: Is this also about sending a message that, as we say in America, there's a new sheriff in town?

Mohammed bin Salman: Absolutely. Absolutely.

"Saudi Arabia does not want to acquire any nuclear bomb, but without a doubt, if Iran developed a nuclear bomb, we will follow suit as soon as possible."

But while the "new sheriff" is cracking down on corruption, there are questions about his own fortune. The New York Times reports he recently purchased a yacht for a half-billion dollars, along with a French chateau.

Mohammed bin Salman: My personal life is something I'd like to keep to myself and I don't try to draw attention to it. If some newspapers want to point something out about it, that's up to them. As far as my private expenses, I'm a rich person and not a poor person. I'm not Gandhi or Mandela. I'm a member of the ruling family that existed for hundreds of years before the founding of Saudi Arabia. We own very large lots of land, and my personal life is the same as it was 10 or 20 years ago. But what I do as a person is to spend part of my personal income on charity. I spend at least 51% on people and 49 on myself.

Among the prince's official titles is "minister of defense." And this is where his apparent fixation on Iran has led him into a quagmire in neighboring Yemen.

Mohammed bin Salman: The Iranian ideology penetrated some parts of Yemen. During that time, this militia was conducting military maneuvers right next to our borders and positioning missiles at our borders.

His response was to launch a bombing campaign that's led to a humanitarian disaster, as we reported on 60 Minutes last fall. He says Iranian-backed rebels have used the country to fire missiles at Riyadh.

Mohammed bin Salman: I can't imagine that the United States will accept one day to have a militia in Mexico launching missiles on Washington D.C., New York and LA while Americans are watching these missiles and doing nothing.

The United Nations says thousands of civilian deaths in Yemen are the direct result of Saudi airstrikes and a blockade, since lifted, of Yemen's port that temporarily stopped food and medicine from getting to hundreds of thousands of people.

Norah O'Donnell: Do you acknowledge that it has been a humanitarian catastrophe, 5,000 civilians killed and children starving there?

Mohammed bin Salman: It is truly very painful, and I hope that this militia ceases using the humanitarian situation to their advantage in order to draw sympathy from the international community. They block humanitarian aid in order to create famine and a humanitarian crisis.

Norah O'Donnell: Is what's happening in Yemen, essentially, a proxy war with Iran?

Mohammed bin Salman: Unfortunately, Iran is playing a harmful role. The Iranian regime is based on pure ideology. Many of the Al-Qaeda operatives are protected in Iran and it refuses to surrender them to justice, and continues to refuse to extradite them to the United States. This includes the son of Osama bin Laden, the new leader of Al-Qaeda. He lives in Iran and works out of Iran. He is supported by Iran.

Saudi Arabia's Crown Prince Mohammed bin Salman with contributor Norah O'Donnell CBS News

It's worth noting that Sunni Saudi Arabia and Shia Iran both claim to represent the one true branch of Islam.

Norah O'Donnell: At its heart, what is this rift about? Is it a battle for Islam?

Mohammed bin Salman: Iran is not a rival to Saudi Arabia. Its army is not among the top five armies in the Muslim world. The Saudi economy is larger than the Iranian economy. Iran is far from being equal to Saudi Arabia.

Norah O'Donnell: But I've seen that you called the Ayatollah, Khamenei, "the new Hitler" of the Middle East.

Mohammed bin Salman: Absolutely.

Norah O'Donnell: Why?

Mohammed bin Salman: Because he wants to expand. He wants to create his own project in the Middle East very much like Hitler who wanted to expand at the time. Many countries around the world and in Europe did not realize how dangerous Hitler was until what happened, happened. I don't want to see the same events happening in the Middle East.

Norah O'Donnell: Does Saudi Arabia need nuclear weapons to counter Iran?

Mohammed bin Salman: Saudi Arabia does not want to acquire any nuclear bomb, but without a doubt, if Iran developed a nuclear bomb, we will follow suit as soon as possible.

60 Minutes producer Harry Radliffe II CBS News

A note from 60 Minutes: Our story "Heir to the Throne" has many authors. The ten-person team that traveled to Saudi Arabia for approximately a week included correspondent Norah O'Donnell, who carried with her a long-held fascination for the region. Also on our team: producers Graham Messick and Vanessa Fica, who began working on the assignment more than two years ago at the request of the story's original producer, Harry A. Radliffe II, before he passed away of cancer at age 66.

Radliffe was 60 Minutes' resident expert on politics, religion, and history in the Middle East. Well-traveled and passionately curious, Harry would say about a 60 Minutes segment on Saudi Arabia: "If that ain't a story, I don't know what is." Radliffe was known for taking his time with stories like this; he knew that some day, the Saudi royal family would – at long last -- give its go-ahead. Sadly, that day came after Harry's passing, but we are so glad to have carried on his vision.

Also on the team that made this story possible: associate producer Jack Weingart, Middle East producer Amjad Tadros, photographers Jonathan Partridge and Mark La Ganga, audio engineers Anton Van der Merwe and Matt Magratten, and editors Dan Glucksman and Craig Crawford. Jeff Fager, Radliffe's close friend and the executive producer of 60 Minutes, had final say over the story and personally assured two Saudi princes that we would be fair and accurate and allow the crown prince to tell his story if he let us. We are glad he did.

Saudi Arabia's 32-year-old Crown Prince Mohammed bin Salman outmaneuvered uncles, cousins and half-brothers to become the power behind the throne of his aging father, King Salman. Since then, this royal upstart has been remaking Saudi society— out of both social and economic necessity. The vast majority of the kingdom's citizens are under 30 — connected to the world at large through their cell phones. Just as important, oil is no longer a predictable source of revenue, meaning the cradle-to-grave healthcare, education and other services that have been the birthright of every Saudi citizen, are imperiled. It's a combustible mix for a brash leader in a dangerous part of the world. But, the heir to the throne seems eager for the challenge.

Norah O'Donnell: Oh, this is where you spend all night?

Mohammed bin Salman in English: Mostly. So all of the workaholic ministers used to spend most of their nights in this, in these offices. So, I'm sorry if it's a little bit lousy.

Norah O'Donnell: This is not a lousy office.

He spends most evenings in Riyadh's Irgah Palace, where he dispenses with the traditional Saudi headscarf.

Norah O'Donnell: And so what time in the morning are you here till working?

Mohammed bin Salman in English: Oh, I come here, at, like afternoon till late night.

We're told his 82-year-old father, King Salman, is somewhere upstairs, leaving most of the day-to-day work to his son. He escorted us at 9 p.m. into a meeting about the public investment fund.

Under Prince Mohammed's detailed plan to remake Saudi Arabia – called "Vision 2030" – the public investment fund will eventually grow to $2 trillion. The men in this room are talking about how to invest it. They recently sank three and a half billion dollars into Uber. If bets like that pay off, it will be dividends, not oil revenues, pouring into the Saudi treasury.

Princess Reema: This man spend 24 hours a day working towards this vision.

Princess Reema bint Bandar is the crown prince's cousin and he chose her to lead one of the government sports authorities.

Norah O'Donnell: You were surprised by the pace with which he's doing stuff.

Princess Reema: I'm not surprised by the pace. I'm surprised by how detailed the pace is. We are not a community that's used to somebody saying, "Tuesday, the 5th of November, I want to see X." That kind of means yes, maybe, inshallah.

Norah O'Donnell: God willing.

Saudi Arabia's Crown Prince Mohammed bin Salman leads a meeting CBS News

Princess Reema: There is actually a tracking system that we all monthly update. What's our progress? How have we hit our numbers? We are working and operating like a private sector. And that's new.

To a visitor, it doesn't look like that much has changed. Single men in crisp white robes and women dressed entirely in black, keep their distance from one another. Female visitors still feel obligated to wear the traditional Abaya in public… but no longer the headscarf. At this Starbucks, men sit in one section – women and families just beyond the wooden partition.

It was difficult to get people – especially women – to talk on camera about the crown prince's reforms. This man urged caution.

Abdul Rahman: I like the change that is gradual. We don't wanna move too fast and pay a heavy price.

Norah O'Donnell: In other words, you think that the crown prince has to be very careful about the pace?

Abdul Rahman: Exactly.

Saudi Arabia still adheres to an ancient power-sharing arrangement between the House of Saud and Wahhabi Islam, the strict, predominant faith in Saudi Arabia. But the crown prince told us it is not his religion, but extremists within Islamic groups like the Muslim Brotherhood, that have infiltrated Saudi society, including its schools.

Norah O'Donnell: Are you looking at the schooling and the education in Saudi Arabia?

Mohammed bin Salman: Saudi schools have been invaded by many elements from the Muslim Brotherhood organization, surely to a great extent. Even now, there are some elements left. It will be a short while until they are all eradicated completely.

Norah O'Donnell: You say you're going to eradicate this extremism in the education system here?

Mohammed bin Salman: Of course, no country in the world would accept that its educational system be invaded by any radical group.

The crown prince represents the vast majority of the Saudi people – who are overwhelmingly young, restless, and connected to just about everything through their cell phones. They see a kindred spirit in their new iPad-addicted leader.

Norah O'Donnell: Most of the young women that I met are all on Snapchat. They were asking me to join them on Snapchat. This is this is changing this entire culture.

Mohammed bin Salman: I can't claim that I played a role in this. Saudi citizens have always been open to social media and technology.

Young Saudis we talked to at this trendy pop-up burger joint say they are still careful about what they post on Twitter and Instagram, which is why members of the opposite sex connect via private messaging apps like Snapchat and Whatsapp.

Norah O'Donnell: Social media.

MALE #1: It's huge in Saudi Arabia.

MALE #2: This is our escape, yes.

Norah O'Donnell: The phone is your escape?

MALE VOICE: Yes. Social media is.

The crown prince has more pressing concerns, only 22 percent of Saudi women work, and he wants to encourage more to join the workforce.

Mohammed bin Salman: We are working on an initiative, which we will launch in the near future, to introduce regulations ensuring equal pay for men and women.

Norah O'Donnell: But you're talking about equal pay. Women can't even drive in this country. This is the last, last place in the world that women don't have the rights to drive.

Mohammed bin Salman: This is no longer an issue. Today, driving schools have been established and will open soon. In a few months, women will drive in Saudi Arabia. We are finally over that painful period that we cannot justify.

Norah O'Donnell: Certainly, most people hear about the rule that will allow women to drive in June. But there have also existed these guardianship laws that, in order to travel, a woman has to get the permission of a male in her household. It seems so throwback.

Mohammed bin Salman: Today, Saudi women still have not received their full rights. There are rights stipulated in Islam that they still don't have. We have come a very long way and have a short way to go.

He wanted us to see this driving school, at Princess Nourah University, the largest all women's university in the world. The school is preparing to teach 70,000 women how to drive.

These trainers will put women through classes and simulators before having them hit the road.

Norah O'Donnell: How do you get to work or school now?

WOMAN #1: For me, I have a driver. Or, like, my dad or my brother.

WOMAN #2: Driving is just a quick win. It's not everything. It's just representative that we're going in the right direction. It's progress. The trajectory now is just going forward and not backwards.

Norah O'Donnell: You are witnessing history?

WOMEN: (OVERTALK) Yes. Exactly. We are glad to be part of this history.

Princess Reema is also helping make history – she recently opened the gates for Saudi women to attend soccer matches.

Norah O'Donnell: I mean, it was just in 2015 that a Saudi woman was arrested trying to go to a game.

Princess Reema: Yes. Yes. And you know what? I'm proud to say that I was at the first game where that's no longer a reality. How sensational is that to say in two years? In two years the arc has changed.

Norah O'Donnell: People have asked me for my impressions and there's so much that's modern, in terms of infrastructure and American restaurants. But it is still interesting to see that single men eat in one part of the restaurant. And families and women in another.

Princess Reema: Correct.

Norah O'Donnell: It's segregated.

Princess Reema: It is viewed here as the preservation of the privacy of the personal space of the woman. If it comes out to being viewed internationally as disrespectful, that's not the intention. Does it end up sometimes causing obstacles? Yes. But the intent is not disrespect.

Norah O'Donnell: Do you think Mohammed bin Salman is prepared to take the throne?

Princess Reema: I don't think anyone is ever prepared. I think since he was 18 years old he has been groomed for leadership.

His ascension would mark a generational power shift. It was his grandfather, King Abdulaziz, who founded modern Saudi Arabia, and was succeeded by six sons, including the current king, King Salman. The crown prince grew up by his father's side, learning and biding his time.

Norah O'Donnell: What did you learn from your father?

Mohammed bin Salman: Many, many things. He loves history very much. He is an avid reader of history. Each week, he would assign each one of us a book. And at the end of the week, he would ask us about the content of that book. The king always says, "If you read the history of a thousand years, you have the experience of a thousand years."

Mohammed bin Salman is trying to keep pace with a population that's become as familiar with American celebrity culture as they are with the tales of the Prophet Muhammad in the birthplace of Islam. Just as American society transformed during the 1960's, the Saudis are in the midst of their own cultural revolution. The kingdom, the Middle East, and the Islamic world may never be the same.

Norah O'Donnell: You're 32 years old. You could rule this country for the next 50 years.

Mohammed bin Salman: Only God knows how long one will live, if one would live 50 years or not, but if things go their normal ways, then that's to be expected.

Norah O'Donnell: Can anything stop you?

Mohammed bin Salman: Only death.

Produced by Graham Messick and Vanessa Fica. Associate producer, Jack Weingart.