This dissertation addresses two distinct topics in the general area of early universe cosmology. The first topic pertains to gravitational wave emissions from cosmic strings. Cosmic Strings are one-dimensional topological defects predicted in a variety offield theories undergoing a phase change due as the Universe cools. Effectively one-dimensional macroscopic objects may also arise in string theory. In both scenarios the expansion of the Universe leads to a scaling regime of complicated interconnected processes in which the strings generate gravitational wave emission. Our work investigates a particular process in the lifespan of cosmic strings - intercommutation - and the associated gravitational wave emission which we compare to that of the standard process of string evaporation. The second topic concerns the collapse of a massive scalar field under self-gravity to form black holes. A bounded region of excess vacuum energy density can, under certain initial conditions, collapse into a black hole and, under other conditions, dissipate away completely. Our work numerically studies this entire process, chalking out the parameter space that leads to collapse vs dissipation. This can serve as a toy model for exploration of possible black hole masses that might be formed in the early universe.