Abstract: In this work, we provide a quick introduction to the classical results about propositional logic, first-order logic, proof system and (basic) model theory, for the readers who are familiar with (informal) set theory and logic. We will cover the completeness theorem of first-order logic, the compactness theorem, Tarski’s undefinability theorem and Gödel’s incompleteness theorem, and is suitable for mathematics or computer science students who are interested in mathematical logic.