A Friendly Introduction To Mathematical Logic by Timothy Leary

An accessible, undergraduate-level introduction to formal logic that builds from the basics of propositional and first-order languages through syntax, semantics, and proof systems, using clear explanations, examples, and exercises to make abstract ideas intuitive; topics include natural deduction and proof techniques, the completeness and compactness theorems, basic model-theoretic notions, an introduction to computability (Turing machines and recursive functions), and a presentation of Gödel’s incompleteness phenomena, all written in a pedagogical, reader-friendly tone.