  Spin networks, essentially labeled graphs, are ``good quantum numbers'' for
the quantum theory of geometry. These structures encompass a diverse range of
techniques which may be used in the quantum mechanics of finite dimensional
systems, gauge theory, and knot theory. Though accessible to undergraduates,
spin network techniques are buried in more complicated formulations. In this
paper a diagrammatic method, simple but rich, is introduced through an
association of 2 by 2 matrices to diagrams. This spin network diagrammatic
method offers new perspectives on the quantum mechanics of angular momentum,
group theory, knot theory, and even quantum geometry. Examples in each of these
areas are discussed.
