Shape theory

Shape theory was founded by K. Borsuk 50 years ago. It is essentially a spectral homotopy theory and occupies an important place in geometric topology. This paper presents the basic concepts and the most important, in our opinion, results of shape theory. Unfortunately, due to space limitation, it is not possible to cover many other interesting problems and results related to this theory. For a more detailed and systematic study of the issues considered in the review, we provide an extensive list of references at the end.