Introduction to Smooth Manifolds

Introduction to Smooth Manifolds is a graduate-level textbook designed to equip students with the essential tools for using manifolds in mathematical or scientific research. The book covers a wide range of topics, including smooth structures, tangent vectors, vector bundles, and more, all presented in a concrete and intuitive manner. The second edition has been extensively revised, with key topics like the rank theorem and the fundamental theorem on flows introduced earlier to enhance understanding. New topics such as Sard’s theorem, transversality, and contact structures have also been added to broaden the scope. Prerequisites include general topology, the fundamental group, covering spaces, and basic undergraduate linear algebra and real analysis. /n/n The approach taken in this book is both practical and rigorous, making it an invaluable resource for students and researchers alike. With its focus on geometric intuition and modern mathematical tools, the book aims to bridge the gap between abstract concepts and real-world applications. Whether you're new to the subject or looking to deepen your understanding, this textbook provides a solid foundation in the theory of smooth manifolds.