ABSTRACT
This chapter introduces an algebraic structure named the quandle. A quandle can be associated with an oriented virtual knot diagram. Equivalent oriented virtual knot diagrams are associated with the same quandle structure; the quandle is an invariant of oriented virtual knots. Invariants based on the quandle are defined using information from the classical crossings; a quandle invariant can distinguish between Kishino's knot and its flip. Before introducing quandles, we study tricoloring of virtual knot diagrams. Tricoloring a virtual knot diagram allows to distinguish the trefoil from the unknot. A coloring of a diagram with only one element is a trivial coloring. A coloring using all three colors is a non-trivial coloring. The additional relations are equations that can be used to determine equality between expressions.
