  We present a novel analysis of the boundary integral operators associated to
the wave equation. The analysis is done entirely in the time-domain by
employing tools from abstract evolution equations in Hilbert spaces and
semi-group theory. We prove a single general theorem from which well-posedness
and regularity of the solutions for several boundary integral formulations can
be deduced as particular cases. By careful choices of continuous and discrete
spaces, we are able to provide a concise analysis for various direct and
indirect formulations, both at the continuous level and for their
Galerkin-in-space semi-discretizations. Some of the results here are
improvements on previously known results, while other results are equivalent to
those in the literature. The methodology presented here greatly simplifies the
analysis of the operators of the Calderon projector for the wave equation and
can be generalized for other relevant boundary integral equations.
