Pluripotential theory is a recently developed non-linear complex counterpart of classical potential theory. Its main area of application is multidimensional complex analysis.The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampère operator. The interplay between these two notions provides the focal point of this monograph, which contains an up-to-date account of the developments from the large volume of recent work in this area.The substantial proportion of this monograph devoted to classical properties of subharmonic and plurisubharmonic functions makes the pluripotential theory available for the first time to a wide audience of analysts.