Mathematical Logics is an introductory yet complete work, centered on the development of classical first order logic. It begins with considerations on paradoxes and (meta)language, also presenting chapters and appendices on classical propositional logic, set theory (naive and formalized), constructions of numerical sets, and Boolean algebras. The author intends to present to undergraduate or graduate students the fundamentals of first order logic, showing how it can be used to formalize mathematics and make more precise definitions, notations and demonstrations that appear in it. All concepts are presented and explained in the text, however, to keep up with fluent reading, it is advisable for the reader to have some experience in informal mathematical demonstrations, acquired in disciplines such as algebra, linear algebra and real analysis.