A differential equation is an equation, which contains at least one (ordinary or partial) derivative of an unknown function. There are different types of differential equations including ordinary differential equations, linear differential equations, partial differential equations, homogeneous differential equations, non-linear differential equations, and non-homogeneous differential equations. Differential equations can also be classified based on the order or coefficients of the derivatives, which may be either constants, or functions of the independent variable. These equations have several applications in fields such as physics, engineering, biology and applied mathematics. An evolution equation refers to a partial differential equation that describes the evolution of a physical system starting from a given initial data with respect to time. Researchers come across a variety of mathematical models that involve the use of evolutionary differential equations, both partial and ordinary, in multiple applications such as mathematical finance, fluid flow, image processing and computer vision, mechanical systems, relativity, physics-based animation, and Earth sciences. This book presents the complex subject of evolutionary differential equations in the most comprehensible and easy to understand language. It attempts to assist those with a goal of delving into the field of mathematics.