The book "Introduction to Perturbation Methods" by Mark H. Holmes, published by Springer, serves as an introduction to the systematic construction of approximations for problems that are otherwise intractable. The methods rely on the presence of a small parameter, which is common in applied mathematics. The book covers a wide range of topics, including asymptotic approximations, matched asymptotic expansions, multiple scales, the WKB method, and the method of homogenization. Each chapter introduces fundamental ideas and applies them to various problems, such as ordinary differential equations, partial differential equations, and difference equations. The book also includes exercises and applications from the research literature, with solutions available on the author's website. The second edition has been updated with new material, including approximations for weakly coupled oscillators, analysis of problems involving transcendentally small terms, and expanded discussions on Kummer functions and metastability. The content is designed to provide a comprehensive understanding of perturbation methods and their applications in solving complex problems.The book "Introduction to Perturbation Methods" by Mark H. Holmes, published by Springer, serves as an introduction to the systematic construction of approximations for problems that are otherwise intractable. The methods rely on the presence of a small parameter, which is common in applied mathematics. The book covers a wide range of topics, including asymptotic approximations, matched asymptotic expansions, multiple scales, the WKB method, and the method of homogenization. Each chapter introduces fundamental ideas and applies them to various problems, such as ordinary differential equations, partial differential equations, and difference equations. The book also includes exercises and applications from the research literature, with solutions available on the author's website. The second edition has been updated with new material, including approximations for weakly coupled oscillators, analysis of problems involving transcendentally small terms, and expanded discussions on Kummer functions and metastability. The content is designed to provide a comprehensive understanding of perturbation methods and their applications in solving complex problems.