On the AKSZ formulation of the Poisson sigma model

We review and extend the Alexandrov-Kontsevich-Schwarz-Zaboronsky construct ion of solutions of the Batalin-Vilkovisky classical master equation. In pa rticular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin-Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown i n a previous paper, the perturbative quantization of this model is related to Kontsevich's deformation quantization of Poisson manifolds and to his fo rmality theorem. We also discuss the action of diffeomorphisms of the targe t manifolds.