Homotopical Topology
Anatoly Fomenko, Dmitry Fuchs
Springer
Updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand
Presents material concisely but rigorously
Illuminates the subject matter with a range of technical and artistic illustrations, along with a wealth of examples and computations meant to provide a treatment of the topic that is both deep and broad
Contains an entirely new chapter on K-theory and the Riemann-Roch theorem

This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).

Topics
Category Theory, Homological Algebra
K-Theory
Algebraic Topology