This chapter explores First-Order Logic, an extension of Propositional Logic, which was the focus of Chapter 1. First-Order Logic takes into account the inner logical structure of proposition resulting from the presence of quantifiers and from specifying individuals, properties, and relations. After showing how to read and write sentences using the symbolism of First-Order Logic, the chapter discusses the need for and use of interpretations in its semantics. Based on that, natural deduction inference rules for identity and for the universal and existential quantifiers are given. As in Chapter 1, developing an understanding of mathematical proof strategies based upon these rules is the end goal of this study. The chapter concludes by comparing formal and informal modes of proof in mathematics and reflecting upon the value of logic for constructing proofs.