Abstract: People have experimented with knotted ropes since ancient times. More formally, there is now a broad and rich mathematical theory of knots. This theory has important connections to other branches of mathematics and to other sciences as well.

From one point of view, though, classical knot theory is only a special case of a more complex subject: the knotting of graphs (i. e. 1-complexes) in 3-space. I’ll describe some interesting examples and discuss the problem of determining when a finite graph in 3-space is unknotted, i. e. the graph can be moved in 3-space so that it lies on the plane.