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This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra. From the reviews:





"This book presents the most important aspects of modern topology, essential subjects of research in algebraic topology ... . The book contains all the key results of basic topology and the focus throughout is on providing interesting examples that clarify the ideas and motivate the student. ... this book contains enough material for two-semester courses and offers interesting material for undergraduate-level topology, motivating students for post-graduate study in the field and giving them a solid foundation." (Corina Mohorianu, Zentralblatt MATH, Vol. 1079, 2006)


"This text provides a concise and well-focused introduction to point set and algebraic topology. The main purpose is to quickly move to relevant notions from algebraic topology (homotopy and homology). Throughout the book the author has taken great care to explain topological concepts by well-chosen examples. It is written in a clear and pleasant style and can certainly be recommended as a basis for an introductory course on the subject." (M. Kunzinger, Monatshefte fur Mathematik, Vol. 152 (1), 2007)

Essential Topology

Continuous Functions.- Topological Spaces.- Topological Properties.- Deconstructionist Topology.- Homotopy.- The Euler Number.- Homotopy Groups.- Simplicial Homology.- Singular Homology.- More Deconstructionism.