Preface PART A I Introduction 1.An Example from Group Theory 2.An Example from the Theory of Equivalence Relations 3.A Preliminary Analysis 4.Preview II Syntax of First-Order Languages 1. Alphabets 2.The Alphabet of a First-Order Language 3.Terms and Formulas in First-Order Languages 4.Induction in the Calculus of Terms and in the Calculus of Formulas 5.Free Variables and Sentences III Semantics of First-Order Languages 1.Structures and Interpretations 2.Standardization of Connectives 3.The Satisfaction Relation 4.The Consequence Relation 5.Two Lemmas on the Satisfaction Relation 6.Some Simple Formalizations 7.Some Remarks on Formalizability 8.Substitution IV A Sequent Calculus 1.Sequent Rules 2.Structural Rules and Connective Rules 3.Derivable Connective Rules 4.ntifier and Equality Rules 5.Further Derivable Rules and Sequents 6.Summary and Example 7.Consistency V The Comleess Theorem 1.Henkin's Theorem 2.Satisfiability of Consistent Sets of Formulas (the Countable Case) 3.Satisfiability of Consistent Sets of Formulas (the General Case) 4.The Comleess Theorem VI The Lowenheim-Skolem and the Compactness Theorem 1.The Lowenheim-Skolem Theorem 2.The Compactness Theorem 3.Elementary Classes 4.Elementarily Equivalent Structures VII The Scope of First-Order Logic 1.The Notion of Formal Proof 2.Mathematics Within the Framework of First-Order Logic 3.The Zermelo-Fraenkel Axioms for Set Theory 4.Set Theory as a Basis for Mathematics VIII Syntactic Interpretations and Normal Forms 1.Term-Reduced Formulas and Relational Symbol Sets 2.Syntactic Interpretations 3.Extensions by Definitions 4.Normal Forms