The Theorem of Pythagoras -- Greek Geometry -- Greek Number Theory -- Infinity in Greek Mathematics -- Number Theory in Asia -- Polynomial Equations -- Analytic Geometry -- Projective Geometry -- Calculus -- Infinite Series -- The Number Theory Revival -- Elliptic Functions -- Mechanics -- Complex Numbers in Algebra -- Complex Numbers and Curves -- Complex Numbers and Functions -- Differential Geometry -- Non-Euclidean Geometry -- Group Theory -- Hypercomplex Numbers -- Algebraic Number Theory -- Topology -- Simple Groups -- Sets, Logic, and Computation -- Combinatorics.

From the reviews of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." (European Mathematical Society) "Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact." (Denis Bonheure, Bulletin of the Belgian Society) This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.