The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: * special geometry and supersymmetry * generalized geometry * geometries with torsion * para-geometries * holonomy theory * symmetric spaces and spaces of constant curvature * conformal geometry * wave equations on Lorentzian manifolds * D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kähler geometry or generalized geometry.