This book, "An Introduction to Semilinear Evolution Equations" by Thierry Cazenave and Alain Haraux, revised by Yvan Martel, provides a comprehensive introduction to the theory of semilinear evolution equations. The content is divided into several chapters, covering essential topics such as preliminary results, $m$-dissipative operators, the Hille–Yosida–Phillips Theorem, and applications to various partial differential equations. Key areas of focus include the heat equation, the Klein–Gordon equation, and the Schrödinger equation, with detailed discussions on local and global existence, blow-up in finite time, and stability of solutions. The book also explores abstract dynamical systems, Liapunov functions, and the invariance principle, providing a solid foundation for understanding the behavior of semilinear evolution equations.This book, "An Introduction to Semilinear Evolution Equations" by Thierry Cazenave and Alain Haraux, revised by Yvan Martel, provides a comprehensive introduction to the theory of semilinear evolution equations. The content is divided into several chapters, covering essential topics such as preliminary results, $m$-dissipative operators, the Hille–Yosida–Phillips Theorem, and applications to various partial differential equations. Key areas of focus include the heat equation, the Klein–Gordon equation, and the Schrödinger equation, with detailed discussions on local and global existence, blow-up in finite time, and stability of solutions. The book also explores abstract dynamical systems, Liapunov functions, and the invariance principle, providing a solid foundation for understanding the behavior of semilinear evolution equations.