Editor's Note: On August 20, 2020, Navalny was admitted to a hospital in Russia after losing consciousness on a flight. Doctors said they were working to save his life after he went into a coma and was put on a ventilator in intensive care. His supporters claim he was poisoned because of his political activities.

A lot's been said about Russia meddling in our 2016 presidential campaign. But the Russians are already buzzing about their presidential election next March. Because unexpectedly Vladimir Putin has a genuine challenger: a handsome, 41-year-old lawyer, Alexey Navalny, who has chosen one of the most dangerous occupations in the world: running against the man who controls the Kremlin.

"During my campaign, I spent every fifth day in the jail. So now I'm kind of, you know, used to it."

The election process in Russia is tightly managed by the government, but Navalny's been drawing big crowds to his protests and rallies all over the country - where he laces into Putin with no holds barred.

Alexey Navalny at a rally (Translation): Putin is a thief and the head of the entire corrupt system!

This is one brave man. Not only because he has taken on the all-powerful Vladimir Putin head on, but because he's been holding rallies -- many of them without official permits -- which has had its consequences: one arrest after another.

Alexey Navalny: During my campaign, I spent every fifth day in the jail. So now I'm kind of, you know, used to it. It's become a routine of my life.

Lesley Stahl: You got out of prison just a couple of days ago.

Alexey Navalny: Right.

Lesley Stahl: You held a rally right away. You're goading them. You're begging them to arrest you again.

Alexey Navalny: These are people who are trying to steal my country. And I strongly disagree with it. I'm not going to be, you know, a kind of speechless person right now. I'm not going to keep silent.

Correspondent Lesley Stahl walks with Alexey Navalny CBS News

Lesley Stahl: You're not allowed to run.

Alexey Navalny: I'm not allowed to run. And they put enormous pressure on our headquarter and on our volunteers. My chief of campaign get out of jail just yesterday. So all these facts show us that he's really afraid. Not of me but this -- people who are standing behind me. We have now 170,000 volunteers.

Mr. Putin remains highly popular. It's all but a foregone conclusion that he'll be re-elected. And yet the Kremlin is doing everything it can to make it difficult for Navalny to gain traction. For instance, the government says he can't be on the ballot because he was found guilty of embezzlement, in what Navalny insists was a trumped-up charge.

And he's barred from national television. But he's managed to get around that by reaching an ever-widening audience on social media channels and YouTube where he has millions of followers and says he's raised almost $4 million from ordinary Russians.

Lesley Stahl: What do you think the biggest issue is for most people here in Russia?

Alexey Navalny: Poverty. And inequality, huge in Russia, even compared to the United States, the European country. No opportunities at all, no future for the people. Putin is stealing their future. And Mr. Putin [makes] his relatives, his closest friends, his colleagues from the KGB -- the chiefs of these companies. And that's why they're controlling the whole economy.

Navalny began his public life ten years ago in a shrewd way: he bought small shares of state-owned companies. As a shareholder, he was able to get his hands on internal financial documents, investigated evidence of misconduct and posted it all on a blog.

Alexey Navalny CBS News

Lesley Stahl: Did these documents that you got prove corruption?

Alexey Navalny: Absolutely. I work as a whistleblower. And I'm not afraid to announce the names.

He says he found that the Kremlin's inner circle was accumulating vast amounts of wealth and published pictures of multiple homes and yachts. He moved on to airing documentaries on YouTube, with video of the officials' lavish lifestyle.

Lesley Stahl: How did you get the footage?

Alexey Navalny: We have our air force. We're just using drones.

Lesley Stahl: You sent drones up?

Alexey Navalny: Yes. We do a lot of work with the drones because for us, it's best way to show this way of life. When you publish this footage of the yachts, of these palaces, of this real estate and you can show documents, look, this guy have a relatively modest salary but look at this house.

His most-watched documentary, with over 25 million views, focused on Prime Minister Dmitry Medvedev and his estates -- Navalny says all 5 of them.

The video inflamed so much outrage that in March tens of thousands of Russians took to the streets. When Navalny called for a second round of protests 3 months later, he was arrested before he even left his apartment building.

But his supporters came out in droves all across the country and, like Navalny, close to 1700 were arrested. These were the first protests of this magnitude in Russia in 6 years.

Back then, in 2011, roughly 60,000 went to the streets in a burst of anti-Putin dissent. That's when Navalny debuted in Moscow as an opposition leader.

Lesley Stahl: As we were watching in the United States I think there was the impression that public opinion was going to force change here. It looked that way on television. But that is not what happened.

Alexey Navalny: Mr. Putin realized that he's-- it's not affordable for his system to give people more democracy. That's why in 2012 he completely change his strategy and start to arrest people, start to fabricate criminal cases. Look, at the start of the 2011 I was a respectful lawyer. At the end of 2012 I was several times convict.

But now he's seen as the last man standing since most of the other opposition leaders either fled the country or were found dead under mysterious circumstances.

Alexey Navalny and correspondent Lesley Stahl CBS News

Lesley Stahl: Why are you still alive?

Alexey Navalny: This is the favorite question of my wife... I don't know. Maybe they missed the good timing for it when I was less famous?

Lesley Stahl: Do you feel that your visibility with so many people knowing who you are that that's protecting you?

Alexey Navalny: Actually, I'm trying not to thinking about it a lot. Because if you start to think what kind of risks I have, you cannot do anything.

"My biggest memory that I'm as a child standing in line, standing in line maybe sometimes for hours to just buy milk."

Navalny's platform includes: more spending on education and health, restoring a free press and taxing the oligarchs. In the west he's assumed to be a Russian liberal, but there was a time when he marched with nationalists, some of them fascists -- something he's tried to downplay lately.

Lesley Stahl: You have attended Nationalist, what we would call right-wing rallies, I believe in support of ethnic purity, Russian ethnic purity. Have you supported that?

Alexey Navalny: Of course not. I was part of these rallies because I support the freedom of rallies because I support freedom for meetings.

Lesley Stahl: They're supporters of yours. They're part of your following.

Alexey Navalny: A lot of them supports me. And they recognize me as a leader.

When he was growing up, he came from a committed communist family in a small town, south of Moscow.

Lesley Stahl: What was your childhood like?

Alexey Navalny: I'm 41 years old. It means that actually, I'm a guy from the Soviet Union. I was a young pioneer. I had my red tie. My father was military and I was very proud that my father is guarding Mother Russia from evil Americans with their bombs and missiles. Actually, my biggest memory that I'm as a child standing in line, standing in line maybe sometimes for hours to just buy milk.

He was close to his brother, Oleg, 7 years younger. So it was painful for him when 3 years ago the government, to get him to stop his activism he believes, convicted him and Oleg of embezzlement,

A ruling the European Court of Human Rights called "arbitrary and unfair." To make matters worse, he got a suspended sentence, but Oleg is still behind bars.

Alexey Navalny CBS News

Alexey Navalny: He's still in prison. And he spent two years in the solitary confinement which actually in Russian condition is torturing.

Lesley Stahl: Do you think he's in jail to get you, to get you to stop?

Alexey Navalny: Yes, absolutely.

But he hasn't stopped, even though he's been physically attacked. While campaigning in Siberia, he was splashed in the face with green dye.

Alexey Navalny: It was painful. But I could--

Lesley Stahl: It hurt?

Alexey Navalny: It hurt.

But -- he handled it with humor saying he was Shrek.

His followers dyed their own faces green and posted photos to Instagram and Twitter in solidarity.

Then he was splashed again.

Alexey Navalny: The second time it was much more painful.

Lesley Stahl: There was acid, as I understand it

Alexey Navalny: My doctor in the hospital said, "Well, Alexey, you should be prepared that you will be blind for one eye." And so I even start to think about kind of, you know, I will be such kind of pirate with.

Lesley Stahl: With a patch.

Alexey Navalny: With a patch.

The Kremlin did allow him to travel to Spain for specialized surgery. But immediately after the treatment, he returned to Moscow and went right out campaigning again.

But lately, he's been concentrating on rural areas, holding rallies far from the big cities -- in places like Siberia and the Urals.

Alexey Navalny on platform: I'm travelling every weekend to spend Friday, Saturday and Sunday in the regions to have these rallies.

On our last day there, we went with him to the mid-sized, industrial city of Ivanovo, four hours outside Moscow – starting with a train ride.

Lesley Stahl: Mr. Putin never ever mentions your name. May criticize you but never your name. What do you make of that?

Alexey Navalny: I have no idea why they don't. Maybe it's a kind of something superstitious for them. Like, you know, you cannot name the animal bear, because if you name it in the night, it will come and eat you or something like this. They have a lot of nicknames and euphemisms for me. Like "this gentleman" or "this guy," "this convict," and "this--"

Lesley Stahl: This convict?

Alexey Navalny: "This convict." but-- they are thinking about me. And believe me, they are afraid of me, afraid of us. So it's-- that is much more important for us than mentioning my name.

It was snowing and dark out when we got to a wooded lot on the edge of town where a big crowd of mostly young Russians was waiting. No one thinks he has much of a chance of beating Putin in the election, but still Putin fears him, Navalny says, because of his ability to draw crowds at rallies and into the streets.

He perseveres, knowing what he's doing is dangerous. His supporters have been roughed up by police and pro-Kremlin activists who Navalny calls thugs.

Lesley Stahl: Is it, in your mind, worth your life? Because there is a big target on you, no question.

Alexey Navalny: I'm tryin' to not think about it. Because look, I think I'm ready to sacrifice everything for my job, and for the people who surrounding me. I'm not let them down. And I'm trying to not to reflects about it all the time.

Produced by E. Alexandra Poolos. Associate Producer, Kate Morris.