ABSTRACT
Virtual knot theory was proposed by Louis H. Kauffman. Virtual crossings arise as artefacts of such a projection; that is, intersection points of images of arcs, non-intersecting in Sg and classical crossings appear just as projections of crossings. In the very beginning of this theory, the creators have proposed generalisations of some basic knot invariants: the knot quandle, the fundamental group, the Jones polynomial. Virtual Reidemeister moves give a new equivalence relation for classical links: there exist two isotopies for classical links, the classical one that we are used to working with, and the virtual one. Each virtual knot can be transformed to another one by using all generalised Reidemeister moves and all versions of the forbidden moves. There are two approaches to the finite type invariants of virtual knots: the one proposed by M. N. Goussarov, M. Polyak and O. Ya. Viro and the one proposed by Kauffman.
