This volume comprises 8 articles written by lecturers of 50th Karpacz Winter School of Theoretical Physics and their collaborators. The contributing lecturers are outstanding researchers, and experts in various fields of physics, in particular in condensed matter, quantum phase transitions and quantum critical phenomena. The articles reflect the contents of the lectures given for school participants and cover various aspects of quantum phase transitions and quantum critical phenomena, from experimental to mathematical ones. For those wishing to get acquainted with the subject, extensive lists of references are provided in the articles.