This book presents a variety of methods of analytic solution of ordinary differential equations and features a wealth of examples, both solved in detail and proposed. The goal of this work is to give a broad training in techniques of solution of equations and problems involving differential equations, which are important both in mathematics and applications. The book is aimed primarily at undergraduate students of mathematics, natural sciences and engineering, who need a solid knowledge of differential equations in their professional activities. The text contains many examples of scientific problems solved by constructing models involving differential equations, which introduce students to a number of interesting aspects of applications. The proposed material can also be useful for professors and instructors of differential equations courses, since the text contains an exposition of all the principal analytic techniques usually studied in undergraduate programs, which are illustrated with numerous examples. In this way, teachers/instructors can use this book both to teach classes and to administer exams/tests on the studied subjects.