The textbook discusses models of physics, mechanics, chemistry, biology, ecology, economics, sociology, meteorology, electrical engineering, applications to probability theory, game theory, computational mathematics, etc., based on differential and difference equations. This practical guide to sharing analytical and computational approaches also contains tasks of varying complexity for homework and benchmarking, workshops, exams and coursework. The book is written on the basis of a course that the author taught for many years at the Department of Applied Mathematics of the Higher School of Economics, and is addressed to students and graduate students of natural sciences.