  In this thesis we give an overview of the antifield formalism and show how it
must be used to quantise arbitrary gauge theories. The formalism is further
developed and illustrated in several examples, including Yang-Mills theory,
chiral $W_3$ and $W_{2,5/2}$ gravity, strings in curved backgrounds and
topological field theories. All these models are characterised by their gauge
algebra, which can be open, reducible, or even infinitly reducible. We show in
detail how to perform the gauge fixing and how to compute the anomalies using
Pauli-Villars regularisation and the heat kernel method. Finally, we discuss
the geometrical structure of the antifield formalism.
