  Inverse braid monoid describes a structure on braids where the number of
strings is not fixed. So, some strings of initial $n$ may be deleted. In the
paper we show that many properties and objects based on braid groups may be
extended to the inverse braid monoids. Namely we prove an inclusion into a
monoid of partial monomorphisms of a free group. This gives a solution of the
word problem. Another solution is obtained by an approach similar to that of
Garside. We give also the analogues of Artin presentation with two generators
and Sergiescu graph-presentations.
