Vassiliev, here presented in English translation, first presented this material in a 1996 lecture course at Independent Moscow U. The central topic of the classical notions and methods of differential and algebraic topology are distilled into a pithy volume for researchers, specialists, and advanced students in mathematics and theoretical physics. The volume includes treatment of manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, Morse theory, and PoincarT duality. Annotation c. Book News, Inc., Portland, OR (booknews.com)