String theory is a leading candidate for the unification of universal forces and matter, and one of its most striking predictions is the existence of small additional dimensions that have escaped detection so far. This book focuses on the geometry of these dimensions, beginning with the basics of the theory, the mathematical properties of spinors, and differential geometry. It further explores advanced techniques at the core of current research, such as G-structures and generalized complex geometry. Many significant classes of solutions to the theory's equations are studied in detail, from special holonomy and Sasaki–Einstein manifolds to their more recent generalizations involving fluxes for form fields. Various explicit examples are discussed, of interest to graduates and researchers.

'An excellent introduction to the methods and techniques used to study the geometries that could connect string theory to particle physics.'

Prof. Juan Maldacena - Institute for Advanced Study

'This book provides an excellent exposition of the beautiful interplay of geometry and physics arising in string theory and will prove an invaluable introduction to the subject for physicists and mathematicians alike. It presents many of the latest developments and covers topics and details not discussed elsewhere. Written by an expert in the field, this book has a careful pedagogical approach and will be a key text for graduate students and an essential tool for researchers.'

Prof. Chris Hull FRS - Imperial College London

‘Geometry of String Theory Compactifications would be a most appropriate acquisition for a comprehensive university library, especially one supporting an active group of string theory researchers, whether they be in mathematics or physics departments … Recommended.’

M. C. Ogilvie Source: Choice