This tutorial is an introduction to higher mathematics. Quite strictly and formally (at the level of definitions and concepts), but at the same time meaningfully and with examples, the foundations of higher mathematics for non-mathematical specialties are considered. The presentation is accompanied by a large number of specially selected examples explaining the essence of the studied concepts and facts. The textbook is intended for all representatives of "non-physical-mathematical" fields interested in the basics of higher mathematics in order to learn these basics and use them in their work or study.