Resumen en inglés

ABSTRACT: In this monograph, we review the mathematical foundations of the Batalin-Vilkovisky formalism for treating gauge systems, in the context of homological algebra and graded differential geometry. This formalism leads to an L∞-algebra that encodes all the information of a classical field theory: gauge symmetries, field content, equations of motion, and Noether identities. As illustrative examples, we present the Yang–Mills and Chern–Simons theories