Alexey Navalny is President Vladimir Putin's most popular critic, and now he has taken on the Kremlin ruler in a bid for the Russian presidency. The challenges facing this 41-year-old anti-corruption activist are many. The government says Navalny can't run for office and he has been arrested and jailed numerous times for holding rallies without a permit. Attackers threw green dye in his face -- twice -- and he nearly lost sight in one of his eyes. His supporters have been stabbed and beaten. He and his brother have been found guilty of embezzlement, in charges Navalny insists were trumped up. His brother is still in jail, held hostage as punishment for his opposition to Putin, says Navalny. Despite the fact many of Putin's critics have died mysteriously or fled the country, Navalny is determined to make good on his promise to his followers to challenge Putin for the presidency in March 2018. Lesley Stahl interviewed Navalny for a report to be broadcast on the next edition of 60 Minutes, Sunday, Dec. 10 at 7:00 p.m., ET/PT.

Asked by Stahl whether continuing to oppose the Russian leader is worth his life, Navalny responds, "I'm trying not to think about it, because, look, I think I'm ready to sacrifice everything for my job and for the people who [are] surrounding me. I'm not [going to] let them down."

Navalny says he's used to being targeted. "During my campaign, I spent every fifth day in the jail," he tells Stahl. "It's become a routine of my life." Many of the arrests are for holding rallies without permits that attract thousands of supporters. When 60 Minutes came to interview Navalny, he had just gotten out of jail and immediately took to the streets to hold a rally, again. His main message at these rallies, as he said at one, is "Putin is a thief and the head of the entire corrupt system."

The corrupt system is costing Russians their livelihoods, he says, because Putin taps his friends and family to run important companies who put their own enrichment ahead of the country's economic needs. "No opportunities at all. No future for the people," says Navalny. "Putin is stealing their future."

The Russian government says the crime Navalny was convicted of, that he denies committing, embezzlement, precludes him from running for president. He is barred from national television. But Navalny has used social media and YouTube to spread his message, gaining millions of followers. He now has 170,000 volunteers working on his campaign, he says. He believes his popularity may have saved his life.

Asked why he is still alive, Navalny says "I don't know. Maybe they missed the good timing for [murdering me] when I was less famous?"