  We discuss the theory of knots, and describe how knot invariants arise
naturally in gravitational physics. The focus of this review is to delineate
the relationship between knot theory and the loop representation of
non-perturbative canonical quantum general relativity (loop quantum gravity).
This leads naturally to a discussion of the Kodama wavefunction, a state which
is conjectured to be the ground state of the gravitational field with positive
cosmological constant. This review can serve as a self-contained introduction
to loop quantum gravity and related areas. Our intent is to make the paper
accessible to a wider audience that may include topologists, knot-theorists,
and other persons innocent of the physical background to this approach to
quantum gravity.
