  We describe in this chapter (Chapter IX) the idea of building an algebraic
topology based on knots (or more generally on the position of embedded
objects). That is, our basic building blocks are considered up to ambient
isotopy (not homotopy or homology). For example, one should start from knots in
3-manifolds, surfaces in 4-manifolds, etc. However our theory is, until now,
developed only in the case of links in 3-manifolds, with only a glance towards
4-manifolds. The main object of the theory is a skein module and we devote this
chapter mostly to the description of skein modules in 3-dimensional manifolds.
  H. Poincare, in his paper "Analysis situs" (1895), abstractly defined
homology groups starting from formal linear combinations of simplices, choosing
cycles and dividing them by relations coming from boundaries The idea behind
skein modules is to use links instead of cycles (in the case of a 3-manifold).
More precisely we consider the free module generated by links modulo properly
chosen (local) skein relations.
