Developing and providing an overview of recent results on nearly Kähler geometry on
pseudo-Riemannian manifolds this monograph emphasizes the differences with the classical
Riemannian geometry setting. The focal objects of the text are related to special holonomy and
Killing spinors and have applications in high energy physics such as supergravity and string
theory. Before starting into the field a self-contained introduction to the subject is given
aimed at students with a solid background in differential geometry. The book will therefore be
accessible to masters and Ph.D. students who are beginning work on nearly Kähler geometry in
pseudo-Riemannian signature and also to non-experts interested in gaining an overview of the
subject. Moreover a number of results and techniques are provided which will be helpful for
differential geometers as well as for high energy physicists interested in the mathematical
background of the geometric objects they need.