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.
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