Alexander- conway polinomials

This work consists of two parts. In the first part of this work, the fundamental group which is the most important functor in low dimensions and its constructions has been studied. In fact, the fundamental group determines the equivalence of manifolds and knots (homeomorphisims and embedding respectively). But the group obtained here are nearly as difficult as homeomorphism problem of the spaces. That?s why it is needed some new invariants to distinguish the groups. On the other hand, the closure of the complement of a tubular neighbourhood of a knot in S^3 or R^3 is a manifold with boundary hence the embedding problem reduces to homeomorphism problem. Furthermore, for the classical knots in particular equivalence of knots equivalent with equivalence of complements. Unfortunately, this statement is not true in high dimensions. The second part of the work is devoted to an invariant of the fundamental group itself to differentiate the fundamental groups. But invariant we illustrate may be defined in various ways. The method we employ here was given by Conway in early 1980?s, namely, by using Skein theory. This invariant is a Laurent polynomial and known to be Alexander polynomial. But its close relationship with the Skein polynomial of Conway, it is generally called as Alexander - Conway polynomial. End we finished this work by illustrating calculations of Alexander - Conway polynomial for two bridge knots.