| We will discuss various interactions between the theory of reflection groups, both real and complex, and algebraic geometry. In the real case the groups appear in the theory of surface singularities, Cremona transformations and automorphism groups of K3 surfaces over fields of arbitrary characteristic. In the complex case the groups appearin the theory of hypergeometric functions and complex ball uniformizations of moduli spaces of Riemann surfaces of lower genus or cubic hypersurfaces of dimension at most 4. |