This book describes the history of modern mathematics, from the invention of the calculus to the modern era. Addressed not only to those with some knowledge of mathematics but also to those interested in the history of an important part of modern culture, the book provides an image of the complex development of mathematics from the end of the seventeenth century to the Second World War. The discussions take into account the broader social and political currents that affected the development of mathematics, but gives prominence to the development of the ideas of mathematics: the motivations and articulations, the problems and theories that drives the work of mathematicians. The theme of the book comes from Hilbert: "In the history of every mathematical theory three phases can be clearly identified: the creative, the formal, and ultimately, the critical." Bottazzini thus investigates how the developments of mathematics flow into each other, how critical assessment of one theory leads to discoveries of connections to others or to creation of entirely new theories.