ABSTRACT
Classical knots can be obtained as closures of classical braids; virtual knots can be similarly obtained by closing virtual braids. Virtual braids were suggested by Vladimir V. Vershinin. A virtual braid is an equivalence class of virtual braid diagrams by planar isotopies and all virtual Reidemeister moves except the first classical move and the first virtual move. The chapter explains an invariant of virtual braids and shows that the classical braid group is a subgroup of the virtual one. The new "virtual invariant" is very strong: it is stronger than the Burau representation, the Jones-Kauffman polynomial. The closure of a virtual braid is a virtual link diagram. Obviously, isotopic virtual braids generate isotopic virtual links. Furthermore, all virtual link isotopy classes can be represented by closures of virtual braids. As well as virtual knots, virtual braids have a purely combinatorial definition. Namely, one takes virtual braid diagrams and factorises them by virtual Reidemeister moves.
