Ordinary di?erential equations serve as mathematical models for many exciting “real-world” problems, not only in science and technology, but also in such diverse ?elds as economics, psychology, defense, and demography. Rapid growth in the theory of di?erential equations and in its applications to almost every branch of knowledge has resulted in a continued interest in its study by students in many disciplines. This has given ordinary di?er- tial equations a distinct place in mathematics curricula all over the world and it is now being taught at various levels in almost every institution of higher learning. Hundredsofbooksonordinarydi?erentialequationsareavailable. H- ever, the majority of these are elementary texts which provide a battery of techniquesfor?ndingexplicitsolutions. Thesizeofsomeofthesebookshas grown dramatically—to the extent that students are often lost in deciding wheretostart. Thisisallduetotheadditionofrepetitiveexamplesand- ercises, and colorful pictures. The advanced books are either on specialized topics or are encyclopedic in character. In fact, there are hardly any rig- ousandperspicuousintroductorytextsavailablewhichcanbeuseddirectly in class for students of applied sciences. Thus, in an e?ort to bring the s- ject to a wide audience we provide a compact, but thorough, introduction to the subject in An Introduction to Ordinary Di?erential Equations. This book is intended for readers who have had a course in calculus, and hence it canbeusedforaseniorundergraduatecourse. Itshouldalsobesuitablefor a beginning graduate course, because in undergraduate courses, students do not have any exposure to various intricate concepts, perhaps due to an inadequate level of mathematical sophistication.