  We demonstrate that evolutions of three-dimensional, strongly non-linear
gravitational waves can be followed in numerical relativity, hence allowing
many interesting studies of both fundamental and observational consequences. We
study the evolution of time-symmetric, axisymmetric {\it and} non-axisymmetric
Brill waves, including waves so strong that they collapse to form black holes
under their own self-gravity. The critical amplitude for black hole formation
is determined. The gravitational waves emitted in the black hole formation
process are compared to those emitted in the head-on collision of two Misner
black holes.
