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A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke´s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr´s theory of equivalence of general Dirichlet series.

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1: Elliptic functions. 2: The Modular group and modular functions. 3: The Dedekind eta function. 4: Congruences for the coefficients of the modular function j. 5: Rademacher´s series for the partition function. 6: Modular forms with multiplicative coefficients. 7: Kronecker´s theorem with applications. 8: General Dirichlet series and Bohr´s equivalence theorem.

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From the reviews of the second edition:

"Apostol is an excellent writer of mathematics and the topics that are covered in this book are covered thoroughly in a concise, precise manner. ... the writing is characterized by its easy, readable, fluid style. Each chapter is complemented with a nice set of exercises." (µlvaro Lozano-Robledo, The Mathematical Association of America, June, 2011)

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