Sentential Logic -- Informal Remarks on Formal Languages -- The Language of Sentential Logic -- Truth Assignments -- A Parsing Algorithm -- Induction and Recursion -- Sentential Connectives -- Switching Circuits -- Compactness and Effectiveness -- First-Order Logic -- First-Order Languages -- Truth and Models -- A Parsing Algorithm -- A Deductive Calculus -- Soundness and Completeness Theorems -- Models of Theories -- Interpretations Between Theories -- Nonstandard Analysis -- Undecidability -- Number Theory -- Natural Numbers with Successor -- Other Reducts of Number Theory -- A Subtheory of Number Theory -- Arithmetization of Syntax -- Incompleteness and Undecidability -- Recursive Functions -- Second Incompleteness Theorem -- Representing Exponentiation -- Second-Order Logic -- Second-Order Languages -- Skolem Functions -- Many-Sorted Logic -- General Structures.