  This paper is an introduction to the subject of virtual knot theory, combined
with a discussion of some specific new theorems about virtual knots. The new
results are as follows: We prove, using a 3-dimensional topology approach that
if a connected sum of two virtual knots $K_{1}$ and $K_{2}$ is trivial, then so
are both $K_{1}$ and $K_{2}$. We establish an algorithm, using Haken-Matveev
technique, for recognizing virtual knots. This paper may be read as both an
introduction and as a research paper.
