The provided text is the preface and table of contents for the book "Averaging Methods in Nonlinear Dynamical Systems" by J.A. Sanders, F. Verhulst, and J. Murdock. The book is a second edition revision of the first edition, which was published in 1985. The authors discuss the significant growth in perturbation theory, particularly normal form theory, and highlight the changes, corrections, and updates made in this new edition. Key changes include the addition of new chapters and sections, particularly on averaging methods in dynamical systems and normal form theory, as well as new insights into invariant manifolds and averaging for partial differential equations. The preface emphasizes the goal of establishing the foundations and limitations of averaging methods rigorously, while also acknowledging the rich literature in physics that often provides interesting mathematical ideas and problems. The authors express gratitude to various individuals for their contributions and support during the preparation of the book. The table of contents outlines the structure of the book, covering topics such as basic material and asymptotics, averaging methods for periodic and general systems, attraction, periodic averaging and hyperbolicity, averaging over angles, passage through resonance, and the transition from averaging to normal forms. The book also includes appendices on the history of averaging theory, invariant manifolds, celestial mechanics, and averaging methods for partial differential equations.The provided text is the preface and table of contents for the book "Averaging Methods in Nonlinear Dynamical Systems" by J.A. Sanders, F. Verhulst, and J. Murdock. The book is a second edition revision of the first edition, which was published in 1985. The authors discuss the significant growth in perturbation theory, particularly normal form theory, and highlight the changes, corrections, and updates made in this new edition. Key changes include the addition of new chapters and sections, particularly on averaging methods in dynamical systems and normal form theory, as well as new insights into invariant manifolds and averaging for partial differential equations. The preface emphasizes the goal of establishing the foundations and limitations of averaging methods rigorously, while also acknowledging the rich literature in physics that often provides interesting mathematical ideas and problems. The authors express gratitude to various individuals for their contributions and support during the preparation of the book. The table of contents outlines the structure of the book, covering topics such as basic material and asymptotics, averaging methods for periodic and general systems, attraction, periodic averaging and hyperbolicity, averaging over angles, passage through resonance, and the transition from averaging to normal forms. The book also includes appendices on the history of averaging theory, invariant manifolds, celestial mechanics, and averaging methods for partial differential equations.