This textbook discusses all useful topics in algebraic topology and applications. It contains complete definitions of topics well-explained by suitable examples, explanations, and proofs throughout the book. The book studies major topics on topological groups, transformation groups and configuration spaces, the fundamental group and covering spaces, separation theorems in the plane, the Seifert–van Kampen theorem, simplicial complexes and simplicial homology, delta-complexes and singular homology, classification of surfaces, and applications to calculus.

This book is designed as a textbook for a two-semester course in algebraic topology for upper undergraduate and beginning graduate students. The book is also accessible to junior mathematics majors who have studied
general topology or point-set topology. The essential prerequisites for reading this book are: a basic understanding of fundamental notions of general topology or point-set topology. The reader should know some basic facts about calculus, mainly for functions of one, two and multivariable.