Janos Bolyai (1802-1860) was a mathematician who changed our fundamental ideas about space. As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid’s parallel postulate, and in 1832 he published a 24 page paper that eventually shook the foundations of the 2000-year-old tradition of Euclidean geometry. Bolyai’s Appendix (published as just that–an appendix to a much longer mathematical work by his father) set up a series of mathematical proposals whose implications would blossom into the new field of non-Euclidean geometry, providing essential intellectual background for ideas as varied as the theory of relativity and the work of Marcel Duchamp. In this short book, Jeremy Gray explains Bolyai’s ideas and the historical context in which they emerged, were debated, and were eventually recognized as a central achievement in the Western intellectual tradition. Intended for nonspecialists, the book includes facsimiles of Bolyai’s original paper and the 1898 English translation by G. B. Halstead, both reproduced from copies in the Burndy Library at MIT.