ABSTRACT
This chapter discusses virtual knots and links as equivalence classes of decorated underlying diagrams. Equivalence is determined by a set of diagrammatic moves, and two equivalent diagrams are related by a finite sequence of moves. With this viewpoint, we are free to consider a multiverse of knot theories. The chapter explains the set of markings on the diagrams to construct flat links. A flat crossing is marked by a solid crossing without over- or under-markings. Some experimentation shows that the set of free knots has more than one element. The chapter considers knot theories that were obtained by reducing the amount of information provided by the link diagram. It also considers knot theories with a physical motivation. A singular link diagram is an underlying diagram with n components that has two types of crossings: classical and singular crossings. Singular crossings are indicated by marking solid dots on the crossings.
