  In loop quantum gravity we now have a clear picture of the quantum geometry
of space, thanks in part to the theory of spin networks. The concept of `spin
foam' is intended to serve as a similar picture for the quantum geometry of
spacetime. In general, a spin network is a graph with edges labelled by
representations and vertices labelled by intertwining operators. Similarly, a
spin foam is a 2-dimensional complex with faces labelled by representations and
edges labelled by intertwining operators. In a `spin foam model' we describe
states as linear combinations of spin networks and compute transition
amplitudes as sums over spin foams. This paper aims to provide a self-contained
introduction to spin foam models of quantum gravity and a simpler field theory
called BF theory.
