The book “Elementary theory of analytical functions of one and several complex variables” by Andrei Kartan is an outstanding work that opens the world of complex analysis to the reader with its amazing properties and deep mathematical concepts. Kartan, known for his outstanding research in mathematics, offers readers not just a textbook, but a real intellectual odyssey that immerses in the subtleties and nuances of analytical functions. In his work, the author examines the main aspects of the theory of complex variables, starting with elementary concepts and ending with more complex topics, such as multidimensional functions and their properties. Cartan skillfully combines a rigorous mathematical approach with an accessible presentation, making the book suitable for both students studying mathematics and more experienced researchers seeking to deepen their knowledge in this area. Readers interested in mathematics, physics, engineering and related sciences will find many useful ideas and concepts in this book. Senior students, graduate students and teachers will be delighted with a clear and logical presentation of the material, which makes it easy to absorb complex topics. Cartan also draws attention to the practical application of analytical functions, which makes the book particularly valuable for those who want to see how theoretical knowledge can be applied to real-world problems. The topics raised in the book cover a wide range of issues, from the foundations of the theory of functions of a single variable to more complex concepts such as the Cauchy theorem and circuit integrals. Cartan not only explains how these theories work, but also demonstrates their importance in various fields of science and technology. The reader will be able to see how analytical functions affect the solution of real problems, which gives additional value to the material being studied. Cartan's style is clear and logical, which makes his work available to a wide audience. He skillfully uses examples and illustrations to illustrate complex ideas, which allows the reader to better understand and remember the material. Cartan is also known for his other works, such as "Functions of Complex Variables" and "Geometry and Analysis", which also deserve attention and can complement the study of topics raised in "Elementary Theory". This book will be a real treasure for anyone who wants to deepen their knowledge in the field of complex analysis. It not only broadens the horizons of understanding mathematical concepts, but also inspires further research and discovery. Readers who are looking for high-quality literature on mathematics will definitely appreciate Cartan's work, which combines both theoretical rigor and practical utility. If you are interested in topics such as analytical functions, complex analysis or mathematical physics, this book will become an indispensable source of knowledge for you. Do not miss the opportunity to immerse yourself in the world of complex variables with Andrei Cartan, whose work continues to inspire mathematicians and scientists around the world.