It irritates Kasparov when people ask him how many moves he can see ahead, since the question implies that great chess talent can be reduced to a trick of memory or math. And even though computers fascinate Kasparov, he reserves his harshest criticism for those who fail to trust their human intuition. Chess is not merely calculation, he notes; it requires creativity, understanding of psychology, exhaustive preparation (Kasparov relished the thought that while he was studying, his rivals were asleep), and sheer competitive drive. But even if you have those, could you visualize the game-winning position 15 moves ahead, as Kasparov once did?

The focus on the intricacies of competitive chess does not mean, however, that the book is narrow or written for insiders. Kasparov moves fluidly in and out of the chess world, quoting Churchill, Goethe, and John F. Kennedy without seeming too pretentious. He has a touch for metaphor, as when he likens the endgame in chess to treaty negotiations that take place after a cease-fire. Or when, having explained the importance of coordinating one’s pieces, he observes that “physics tells us ordered systems lose less energy than chaotic systems.” But in such examples, Kasparov is using physics (or diplomacy) to illuminate chess, not the other way around. Knowing that the loss of one bishop weakens the other will not help the physicist. Some of Kasparov’s analogies do not quite ­apply to the world beyond the chessboard because chess is one of the “ordered systems.” Real life is not so neat.

One point that does travel is Kaspa­rov’s debunking of the chestnut “If it ain’t broke, don’t fix it.” He views contentment with alarm, as a step ­toward stagnation. This attitude applies more strictly to chess, in which players strive to improve their position on every move, but it also relates to individual development. In particular, it helps explain a mystery that nearly jumps off every page: Why did Kaspa­rov abandon what was perhaps the greatest chess career of all time to try to democratize Mother Russia, a long-shot prospect at best?

Kasparov, who as a young man tilted against Soviet orthodoxy, is a genuine democrat, and his thoughtfulness will appeal to Western readers. But there is more. “Success,” he confesses, “made me vulnerable.” In life, as over the board (where he displayed an aggressive, risk-prone style), he has thrived on the edge. Thus his advice to highly paid suits: Leave your comfort zone; brush your teeth with your left hand if you have to.

Kasparov says that when Karpov, his rival, faded, he lost the one challenger who consistently pushed him to the edge. He found a new opponent in the I.B.M. computer Deep Blue, which famously beat him—and he sounds as though he’s more bitter about losing to the machine than to any of his human foes.

Now, at 44, he has a new adversary: Putin. Whether Kasparov will ever run for office or merely continue as an organizer is unknowable, but this volume should make clear why Putin ought to regard him with concern. “Garik,” as Kasparov’s mother calls him, does not fight for glory; he fights to win. As he writes of his struggles with the Kremlin’s authoritarian occupant, “There is no losing with grace with such an opponent.” This is a management guru with shark’s teeth.