A differential equation is a mathematical equation containing functions and their derivatives. A function represents a physical quantity, its derivative expresses the rate of change and the equation describes the relationship between the two. Differential equations can be ordinary/partial, linear/non-linear and homogeneous/inhomogeneous. These equations are also described by the order of the highest derivative into first-order, second-order differential equations and so on. These equations are important in engineering, economics, physics and biology. Some notable differential equations are the Laplace equation, the harmonic oscillator differential equation, the Euler-Lagrange equation, heat equation, Black-Scholes equation, etc. This book is a valuable compilation of topics, ranging from the basic to the most complex theories in the field of differential equations. It presents this complex subject in the most comprehensible and easy to understand language. It is an essential guide for both academicians and those who wish to pursue this discipline further.