We offer a definition of iterated elimination of strictly dominated strategies (IESDS) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS by means of a "stability"" criterion, and offer a sufficient and necessary epistemic condition for IESDS. We show by an example that IESDS may generate spurious Nash equilibria in the class of Reny's better-reply secure games. We provide sufficient/necessary conditions under which IESDS preserves the set of Nash equilibria."