Seven Years in Tibet by Heinrich Harrer (1997, Paperback)

I honestly decided to buy it because I loved the movie so much that I wanted to read the memoir from Harrar, himself. The dramatic transformation of his entire character due to the friendship that evolved between himself and the young Dalai Lama was nothing short of amazing. I'm so glad he was free of his old "issues," that he could tell this inspiring and true tale.
The only caveat I would add is that the book has been translated from German. I wish I knew German so the subtle differences of trying to fit the German language perfectly into English would not interfere in any way. I'll never know the answer; perhaps the translator did a wonderful job and it's nothing to be concerned about.