The lectures published in Strasbourg represent the approach of the Hungarian mathematical school in French-speaking area. In accordance with the Hungarian mathematical education this two-volumened work contains the following chapters: Topology, Differential Calculus, Iterative Methods, Functional Analysis, Integral Calculus and Function Spaces.
This method of approach assumes the knowledge of the classic Real Analysis in One Variable. The author pays particular attention to the selection of his subjects, conceives general and aesthetically pleasing mathematical problems with brief and elegant proofs, illustrates his subject with simple but demonstrative examples and provides a detailed bibliography including the original sources of the terms and mathematical problems. The book is completed with a carefully structured name and subject register containing notes that can be helpful to university teachers in selecting their themes.

Vilmos Komornik was a student of – among others - Ákos Császár and László Czách at Eötvös Lorand University, Budapest. His approach and thought way follows the Hungarian mathematical tradition marked by the names of Lipót Fejér, Frigyes Riesz, Pál Turán and Pál Erdős. His work is founded on his six-semester lectures given at Université Louis Pasteur – Strasbourg.