  The present work contains a complete formulation of the Batalin-Vilkovisky
(BV) formalism in the framework of locally covariant field theory. In the first
part of the thesis the classical theory is investigated with a particular focus
on the infinite dimensional character of the underlying structures. It is shown
that the use of infinite dimensional differential geometry allows for a
conceptually clear and elegant formulation. The construction of the BV complex
is performed in a fully covariant way and we also generalize the BV framework
to a more abstract level, using functors and natural transformations. In this
setting we construct the BV complex for classical gravity. This allows us to
give a homological interpretation to the notion of diffeomorphism invariant
physical quantities in general relativity.
  The second part of the thesis concerns the quantum theory. We provide a
framework for the BV quantization that doesn't rely on the path integral
formalism, but is completely formulated within perturbative algebraic quantum
field theory. To make such a formulation possible we first prove that the
renormalized time-ordered product can be understood as a binary operation on a
suitable domain. Using this result we prove the associativity of this product
and provide a consistent framework for the renormalized BV structures. In
particular the renormalized quantum master equation and the renormalized
quantum BV operator are defined. To give a precise meaning to theses objects we
make a use of the master Ward identity, which is an important structure in
causal perturbation theory.
