The collection of problems presented by V. I. Arnold together with comments on their solutions were published (in Russian) in 2000. The collection now appears in English. The second edition is considerably enlarged in both the problems section and the comments section. Almost one third of the book contains statements of the problems and more than two thirds contains comments on the solutions by 59 authors. V. I. Arnold announced his problems twice a year at his Moscow seminar; he also published other problems in his books and papers. These are the sources of the problems collected here. Problems were chosen to stimulate long-term research and many of them are still open and inspiring. The comments describing the present status of the solutions form a very valuable section, describing many interesting branches of contemporary research. They are mostly written by some of Arnold’s former students. The book covers broad aspects of mathematics and it offers interesting and inspiring reading for any mathematician or mathematical physicist.