The purpose of this book is to give a deep understanding of differential equations (DE) and Fourier series. This subject is very important in the field of engineering & Science. This lecture notes will help the students to understand the deep concept of differential equations. At the end, one chapter is given to discussing the Fourier series and Fourier integrals. In addition, a brief discussion about Fourier transforms also given in this book. The topics are divided into 7 chapters. First 4 chapters will discuss the basic definitions, properties, and solvability of the differential equation. Chapter 5, illustrate the methods of solving system of differential equations. Chapters 6 and 7 devoted to studying about Fourier series, Fourier integral and brief about Fourier transforms. Besides solved examples, a number of exercise questions and answers are given at the end of every chapter. In my opinion, this lecture notes will help the students of various universities to understand the deep concepts of the differential equation as this book is designed with simple language and direct examples.