Kim Jong-un's teenage years are recounted in a new biography focusing on his time at a private school in Switzerland.
Putin told Kim that Russia supports his efforts to normalise North Korea's relations with the United States.
A lunch and signing ceremony between the two leaders were scrapped after talks in Hanoi, Vietnam, ended without a deal.
Kim and Trump shook hands and smiled briefly in front of a row of their countries' flags at the Metropole hotel in the Vietnamese capital, Hanoi.
Donald Trump and Kim Jong-un are getting ready for their summit later this week in Vietnam.