In this chapter, we will discuss the structure of mathematical arguments. We begin with an overview of propositional logic. We first introduce propositions and logical operators. Then we discuss tautologies, satisfiability, and logical equivalence. We discuss a propositional calculus that gives us a first glimpse into the method of formal proofs. We sketch the rudiments of predicate logic including universal and existential quantifiers, predicates, and their interpretations. We conclude this chapter with a discussion of basic proof techniques. Furthermore, we will learn how to properly negate statements and how to leverage this knowledge in proofs by contradiction.