Generalized Cohomology

In the 1950s, Eilenberg and Steenrod presented their famouscharacterization of homology theory by seven axioms. Somewhat later, it was found that keeping just the first six of these axioms (all exceptthe condition on the homology of the point), one can obtain manyother interesting systems of algebraic invariants of topologicalmanifolds, such as $K$-theory, cobordisms, and others. Thesetheories come under the common name of generalized homology (orcohomology) theories. The purpose of the book is to give an expositionof generalized (co)homology theories that can be read by a wide groupof mathematicians who are not experts in algebraic topology. It startswith basic notions of homotopy theory and then introduces the axiomsof generalized (co)homology theory