The discovery of superconductivity at 30 K by Bednorz and Muller in 1986 ignited an explosion of interest in high temperature superconductivity. The initial development rapidly evolved into an intensive worldwide research effort - which still persists after more than a decade - to understand the phenomenon of cuprate superconductivity, to search for ways to raise the transition temperature and to produce materials which have the potential for technological applications.During the past decade of research on this subject, significant progress has been made on both the fundamental science and technological application fronts. A great deal of experimental data is now available on the cuprates, and various properties have been well characterized using high quality single crystals and thin films. Despite this enormous research effort, however, the underlying mechanisms responsible for superconductivity in the cuprates are still open to question.This book offers an understanding from the phase transition point of view, surveys and identifies thermal and quantum fluctuation effects, identifies material-independent universal properties and provides constraints for the microscopic description of the various phenomena. The text is presented in a format suitable for use in a graduate level course.