Textbook in PDF format At the beginning in Chapter I, the classical propositional calculus is presented. The logical calculi considered here are based on a system of rules, which define the methods used in proofs from assumptions. The methodological problems in the deductive sciences are given only an elementary treatment. Propositional logic is not sufficient for computer science. And hence, in the next Chapter II, the first-order predicate calculus is initially considered. Some well-known basic notions related to the classical predicate logic are first introduced. As an illustration, by using such formulae, some example mathematical and/or computer science definitions are also described and a set of primitive rules is then presented. In the last Chapter III, elements of set theory are first presented. This theory is a basic tool in discrete mathematics and also in mathematical analysis (concerning infinite sets). Preface The used designations Propositions Predicates Sets Conclusions References