  These introductory lectures show how to define finite type invariants of
links and 3-manifolds by counting graph configurations in 3-manifolds,
following ideas of Witten and Kontsevich. The linking number is the simplest
finite type invariant for 2-component links. It is defined in many equivalent
ways in the first section. As an important example, we present it as the
algebraic intersection of a torus and a 4-chain called a propagator in a
configuration space. In the second section, we introduce the simplest finite
type 3-manifold invariant, which is the Casson invariant (or the
Theta-invariant) of integer homology 3-spheres. It is defined as the algebraic
intersection of three propagators in the same two-point configuration space. In
the third section, we explain the general notion of finite type invariants and
introduce relevant spaces of Feynman Jacobi diagrams. In Sections 4 and 5, we
sketch an original construction based on configuration space integrals of
universal finite type invariants for links in rational homology 3-spheres and
we state open problems. Our construction generalizes the known constructions
for links in the ambient space, and it makes them more flexible. In Section 6,
we present the needed properties of parallelizations of 3-manifolds and
associated Pontrjagin classes, in details.
