In this essay, I define and compare elemental versions of four theories of the firm. These elemental theories are distilled from important contributions by Hart, Holmstrom, Klein, Williamson, and others. Although these contributions have been widely cited and much discussed, I have found it difficult to understand the commonalities, distinctions, and potential combinations of these seemingly familiar contributions. In this essay, therefore, I attempt to clarify these issues, in three steps: I begin with informal summaries of the theories, then turn to simple but formal statements of each elemental theory, and finally nest the four elemental theories in an integrative framework. Keywords: theory of the firm, vertical integration, transaction costs, rent seeking, property rights. JEL Classifications: D23, L14, L22.