This year’s Nobel Prize in Physics was awarded for work in the field of condensed matter physics. The winning Laureate’s pioneering work from the early 1970s and 1980s opened up ways for new and exotic phases of matter, based on the concept of topology, previously used only in mathematics. D. J. Thouless and J. M. Kosterlitz theoretically predicted the existence of unconventional phase transitions in two-dimensional systems. These topological transitions occur at finite temperatures and are governed by dissociation of pairs of nanoscopic topological objects. This scenario explained the mechanism of phase transitions in two-dimensional magnets as well as the occurrence of superconductivity and superfluidity in thin films. F. D. M. Haldane discovered how topological concepts can be used to understand ground-state properties of magnetic chains with integer spin, which belong to the so-called Haldane phase. Another example, which has recently gained a lot of attention, is a topological insulator, a material with non-trivial topological order, which behaves as an insulator in its bulk but whose surface contains topologically protected conducting states. The topological insulator as well as the magnetic chain form the Haldane phase represent symmetry protected by topological states. Over the last decade, this area developed into a frontline research in condensed matter physics, as topological materials could be used in next generation electronics, superconductors and quantum information science. Last but not least, current research reveals secrets of exotic states of matter discovered by this year’s Nobel Laureates., Alžbeta Orendáčová, Slavomír Gabáni, Martin Orendáč., and Obsahuje bibliografii