  This note gives an introduction to Lagrangian field theories in the presence
of boundaries. After an overview of the classical aspects, the cohomological
formalisms to resolve singularities in the bulk and in the boundary theories
(the BV and the BFV formalisms, respectively) are recalled. One of the goals
here (and in [arXiv:1201.0290]) is to show how the latter two formalisms can be
put together in a consistent way, also in view of perturbative quantization.
