Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.Key Features: oAlgebraic Topology is a classical discipline. It is dealt with in various books, but one can think that a new textbook with a very elementary approach should be usefuloNotions are presented in a concrete, ’inductive’ way, starting from elementary examples. Whenever possible, the reader is guided to build the theory through a series of exercises (more than 350), whose solutions are collected in the last chapteroMany references for further reading or study are given

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