This book is addressed to all those who, after finishing the high school, wish a practical initiation in the domain of ordinary differential equations and systems. To provide useful tools for (future) engineers, some elementary problems of mechanics are modeled by using ordinary differential equations. The presentation of notions and results is simplified and made graphically attractive, without loosing the mathematical rigor of the results. To increase accessibility and to encourage the reader to get a technical know-how about ordinary differential equations, each newly introduced notion is accompanied by a series of applications and solved problems. Moreover, each chapter ends by a section containing exercises and problems, with hints and answers. The references contain, along with the books, some links with useful sites, which can be helpful for the reader.