Nobel Lecture, presented on December 8, 2016, at Aula Magna, Stockholm University. In his lecture F. J. M. Kosterlitz described theoretical discoveries of topological phase transitions and topological phases of matter, partially on behalf of the main researcher behind those discoveries, David Thouless, who was not able to give the talk. First, the history of the collaboration between Kosterlitz and Thouless was briefly described. Then, a summary of their contribution to applications of topology to classical Berezinskii-Kosterlitz-Thouless of BKT phase transition was described., John Michael Kosterlitz ; přeložil Ivan Gregora ; foto A. Mahmoud., and Obsahuje bibliografii