In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behavior of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions are boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed on bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview over a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed mat

Pair Correlations in Superfluid Helium 3 In 1996 Lee, Osheroff and Richardson received the Nobel Prize for their 1971 discovery of superfluid helium 3 -- a discovery which opened the door to the most fascinating system known in condensed matter physics. The superfluid phases of helium 3, originating from pair condensation of helium 3 atoms, turned out to be the ideal test-system for many fundamental concepts of modern physics, such as macroscopic quantum phenomena, (gauge-)symmetries and their spontaneous breakdown, topological defects, etc. Thereby they enriched condensed matter physics enormously and contributed significantly to our understanding of various other physical systems, from heavy fermion and high-T_c superconductors all the way to neutron stars and the early universe. A pedagogical introduction is presented. Published as: Published in "Pair Correlations in Many-Fermion Systems", edited by V. Kresin (Plenum, New York, 1998), p. 205-220. arXiv categories: cond-mat