  The notion of Vassiliev algebra in case of hanlebodies is developed. The
analogues of the results of John Baez for links in handlebodies are proved.
That means that there exists a one-to-one correspondence between the special
class of finite type invariants of links in hanlebodies and the homogeneous
Markov traces on Vassiliev algebras. This approach uses the singular braid
monoid and braid group in a handlebody and the generalizations of the theorem
of J. Alexander and the theorem of A. A. Markov for singular links and braids
and the relative version of Markov's theorem.
