Abstract
Aimed at differential geometers, algebraic geometers, and theoretical physicists, in this very elementary and self-contained talk, I will discuss various geometric and physical notions related to manifolds with special holonomy. I will discuss the concept of holonomy; some spin geometry including notions of spinors and Dirac operators; supersymmetry; Calabi--Yau, and manifolds, and some algebraic/analytic constructions. Finally, I will connect all these notions in the context of string theory/M theory/F theory compactifications.