This chapter begins with a detailed exposition of protothetics—the calculus of sentences—and presents a thorough proof of the Compactness Theorem for this calculus as a purely topological result. It then moves on to first-order logic, starting from the notion of a structure, since first-order languages were introduced for the purpose of studying such entities. The chapter includes a detailed presentation of the concept of a model of a first-order language and the related notions of satisfaction and truth. It provides detailed proofs of the Completeness Theorems of Tarski and Gödel, the Compactness Theorem (also known as Maltsev’s Lemma), the Löwenheim–Skolem–Tarski Theorems, and uses the Compactness Theorem to demonstrate the existence of a number field that includes infinitesimal numbers. The chapter concludes with explanations of key concepts in Model Theory such as omitting types, elementary equivalence of models, elementary embeddings, and elementary chains.