 EG keeps the representation of a relation developed here, and remains as Peirce’s final and the most cherished notation for the logic of relations (1903a). EG consists of three parts, Alpha, Beta, and Gamma, which correspond to propositional, first-order, and modal logic, respectively. After presenting the Alpha system in a formal way, we discuss the Beta system of EG focusing on Peirce’s novel ideas in expanding a propositional graphic system to a quantificational graphic system. For more details, we recommend works on EG by Roberts, Zeman, Sowa, and Shin.