  Virtual knot theory is a generalization (discovered by the author in 1996) of
knot theory to the study of all oriented Gauss codes. (Classical knot theory is
a study of planar Gauss codes.) Graph theory studies non-planar graphs via
graphical diagrams with virtual crossings. Virtual knot theory studies
non-planar Gauss codes via knot diagrams with virtual crossings. This paper
gives basic results and examples (such as non-trivial virtual knots with
trivial Jones polynomial), studies fundamental group and quandles of virtual
knots, extensions of the bracket and Jones polynomials, quantum link invariants
with virtual framings, Vassiliev invariants and applications to knots in
thickened surfaces.
