The book is devoted to the theory of differential equations - that branch of mathematics that finds extremely wide and diverse applications in physics and technology. Its author, the largest Italian mathematician Francesco Giacomo Tricomi (1897-1978). The book offered to the reader's attention is written with simplicity, clarity and grace characteristic of the author. Careful selection of material and thoughtful presentation allow, with a relatively small volume, to illuminate many important problems, ideas, methods and results of the modern theory of differential equations, which are usually omitted in general courses.