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).
