This Mathematical Logic course introduces the fundamental concepts of formal reasoning and proof techniques in mathematics and computer science. It begins with a recap of set theory, providing the basic language and tools for logic. The course then covers propositional logic and first-order predicate logic, focusing on syntax, semantics, and the construction of logical arguments. Finally, it explores proof theory, emphasizing formal proof systems and strategies for constructing rigorous proofs. The course aims to develop a strong foundation in logical reasoning essential for advanced studies and applications.