In the monograph "Introduction to the Analysis of Infinite," mathematician Leonard Euler was able to bring the results of many mathematical studies together and, adding his numerous discoveries to them, give the first and exemplary courses of two disciplines at once: the actual introduction to analysis (understanding by this the study of functions using infinite processes generalizing algebraic) and analytical geometry. Collectively, it is a fundamental course, well illustrated with examples, with thoughtful terminology and symbolism. Actually, modern methods of differentiation and integration were first published in the present work of Leonard Euler. For those who are interested in the history of mathematical sciences, for a mathematician-teacher of both secondary and higher education, this book still provides a lot of material for reflection and application.