Nobel Lecture, presented on December 8, 2016, at Aula Magna, Stockholm University. This article describes the history and background of three discoveries cited in this Nobel Prize: The "TKNN" topological formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator of quantum anomalous Hall effect, and its role in the later discovery of time-reversal invariant topological insulators, and the unexpected topological spin-liquid state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topological quantum matter. This article summarizes how these early beginnings have led to the exciting, and currently extremely active, field of "topological matter"., F. Duncan M. Haldane ; přeložil Ivan Gregora ; foto A. Mahmoud, Odile Belmontová., and Obsahuje bibliografii