Algebraic Topology

Algebraic Topology is a foundational textbook designed for graduate-level students and self-study, offering a broad and readable introduction to the subject. It covers essential topics such as the fundamental group, covering spaces, homology, cohomology, higher homotopy groups, and general homotopy theory, with a strong emphasis on geometric aspects to build intuition. The book is unique in its inclusion of many optional topics not typically covered in introductory courses, such as Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces, Hopf algebras, the Brown representability theorem, and a full exposition of Steenrod squares and powers. These additional topics make the book valuable not only for students but also for researchers seeking detailed expositions of advanced subjects. The textbook is structured to facilitate both classroom use and independent study, with numerous examples and exercises to reinforce understanding. The author's clear and engaging writing style makes complex concepts more accessible, while the optional topics provide a deeper exploration for those interested in advancing their knowledge. Whether used in a course or for personal study, Algebraic Topology serves as an indispensable resource for anyone delving into this fascinating field of mathematics.