A survey of the concepts and principles of symbolic logic: valid and invalid arguments, logical relations of statements and their basis in structural features of statements, analysis of the logical structure of complex statements of ordinary discourse, and the use of a symbolic language to display logical structure and to facilitate methods for assessing the logical structure of arguments. We cover the analysis of reasoning with truth-functions ("and", "or", "not", "if ... then") and with quantifiers ("all", "some"), attending to formal languages and axiomatic systems for logical deduction. Throughout, we aim to clearly and systematically display both the theory underlying the norms of valid reasoning and their applications to particular problems of argumentation. The course is an introduction to first-order quantificational logic, a key tool underlying work in foundations of mathematics, philosophy of language and mind, philosophy of science and parts of syntax and semantics. It is largely mathematical and formal in character, but lectures situate these structures within the context of questions raised in contemporary philosophy of language and mind.