  In condensed matter physics and related areas, topological defects play
important roles in phase transitions and critical phenomena. Homotopy theory
facilitates the classification of such topological defects. After a pedagogic
introduction to the mathematical methods involved in topology and homotopy
theory, the role of the latter in a number of mainly low-dimensional
statistical-mechanical systems is outlined. Some recent activities in this area
are reviewed and some possible future directions are discussed.
