This chapter aims to be a short introduction to Poisson geometry which generalizes, in a sense clarified below, the theory of symplectic structures studied in Chap. 1 . More precisely, while every symplectic manifold carries a Poisson bracket (see Formula ( 1.20 )), not every Poisson structure comes from an associated symplectic one. Moreover, it will be shown that every Poisson manifold turns out to be a kind of collage of symplectic manifolds, the ones defining its symplectic foliation.