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We investigate the evolution and interaction of voids in an Einstein-de Sitter universe. Using N-body simulations, we study the growth of different configurations of negative top-hat density perturbations. We find that adjacent voids merge to form larger voids. Thin planar walls form between the merging voids. The peculiar velocity is tangential to a given wall and rises linearly from the wall center. The density contrast of the walls steadily declines as the walls are stretched by the greater rate of expansion within the new void resulting from the merger. A simple hierarchical configuration of negative perturbations demonstrates that smaller scale voids effectively disappear within larger voids as larger scales become nonlinear. The remnants of previous structure formation are frozen in within evolving voids. The evolution of a void is not significantly affected by the collapse of a neighboring positive perturbation of the same scale. The characteristic size of voids which fill the volume of the universe at a given epoch has a narrow distribution suggesting that the large-scale structure appears as a network of close-packed voids of approximately the same size.