Diagrammatic knot theory is an approach to knot theory and surrounding fields in which link diagrams and generalisations are the principal means with which one works with knots, links, 3-manifolds, and other objects in geometric topology. It has a highly combinatorial and pictorial, and sometimes also elementary, flavour.

Starting point

The fundamental result, akin to the Nullstellensatz in algebraic geometry for instance, which makes this approach to knot theory possible is Reidemeister's theorem.

Invariants

Invariants in diagrammatic knot theory are typically obtained by proving invariance under the Reidemeister moves or other collections of moves (usually including at least some of the Reidemeister moves).

Purely diagrammatic fields

Some modern flavours of knot theory, such as virtual knot theory, are defined diagrammatically, although geometric interpretations have sometimes later been found.