This book is intended for students of engineering, applied science, physics, mathematics and of other disciplines, which have the fundamental knowledge of calculus. This has determined the selection of material and the methods of its presentation. The authors emphasize especially the methods for solving individual types of differential equations and the problems leading to differential equations. The mathematical notions they use are exactly defined and assertions are formulated in theorems. Every solution method presented is always illustrated by examples in the text. A number of exercises gives readers the chance of verifying good understanding of the topic. Results to some exercises are given. The contents of the book is divided into 11 chapters: 1. Basis concepts of differential equations. 2. First order differential equations. 3. Linear first order differential equations. 4. Higher order linear differential equations. 5. Systems of linear differential equations. 6. Series solutions. 7. Laplace transformations. 8. Numerical methods. 9. System of autonomous differential equations. 10. Orthogonal functions and Fourier series. 11. Partial differential equations. At the end of the book readers will find Appendix: Determinants and systems of linear equations and Index. The book’s contents is appropriate for a two-semester course. But it is possible to drop out some chapters (e.g. 6,7,8,9,10) without breaking the continuity of the presentation, say, if only one semester is available. The book is very clearly written, so that a brighter student may read it without instructor.