This work is an introduction to mathematical analysis at an elementary level. Emphasis is given to the construction of national and then real numbers, using the method of equivalence classes and of Cauchy sequences. The text includes the presentation of: sequences of real numbers, infinite numerical series, continuous functions, deriviatives and Ramon-Darboux integration. There are also sections on convex functions and on metric spaces, as well as an elementary appendix on logic, set theory and functions.