In these lectures, I will review the Batalin–Vilkovisky formalism (and its cognates) in which the spaces of fields of a physical theory are presented as complexes whose cohomology returns the physical content. Different but equivalent complexes may be used, which turns out to be important conceptually and in practice. A theory of integration (well-defined in the finite-dimensional case) is also available and is the starting point for the quantization of the theories.