Q-Manifolds and Sigma Models

Recent developments of Batalin-Vilkovisky (BV) formalism and related geometry are reviewed. Mathematical structures of BV formalism are summarized as a Q-manifold and a QP-manifold. Lie algebras, Lie algebroids and other higher algebroids are explained as typical examples of Q- and QP-manifolds. Finally, the BV action functionals are constructed by geometric structures of Lie algebroids and Courant algebroids.