The world was shocked when a computer, Deep Blue defeated Gary Kasparov, arguably the greatest human chess player ever to have lived. This remarkable victory, and other, more day-to-day innovations, beg serious questions: what are the limits of what computers can do? Can they think? Do they learn? Discussions of these questions tend to get muddled because most people have only the vaguest idea of how computers actually work. This book explains the inner workings of computers in a way that does not require a profound knowledge of mathematics nor an understanding of electrical engineering. Starting with an account of how computers are built and why they work, W. Daniel Hillis describes what they can and cannot do -- at the present time - before explaining how a computer can surpass its programmer and, finally, where humanity has reached in its quest for a true Thinking Machine.