Donald Sarason
Complex Function Theory (Second Edition) by Donald Sarason is a concise and elegant introduction to the theory of functions of a complex variable. The book emphasizes clarity, rigor, and the development of intuition, making it accessible to advanced undergraduates and beginning graduate students in mathematics. Sarason focuses on core topics such as analytic functions, contour integration, Cauchy’s theorem and formula, power series, and conformal mapping, presenting them with precision and insightful explanations. Unlike many traditional texts, the exposition is streamlined, avoiding excessive technicalities while still providing rigorous proofs. The second edition includes additional exercises and examples to reinforce understanding and encourage problem-solving. Throughout, Sarason highlights connections between complex analysis and other areas of mathematics, such as real analysis and linear algebra, helping readers see the broader context. The book is valued for its readability, logical structure, and ability to convey the beauty and utility of complex function theory. It is suitable both as a classroom text and as a self-study resource for motivated students. Overall, Sarason’s work is celebrated for combining rigor with elegance in presenting a foundational subject of analysis. This book is published by American Mathematical Society (AMS).