This book represents an introductory approach to the theory of Partial Differential Equations and Complex Functions. Nowadays, Partial Differential Equations are one of the most important areas of both Theoretical and Applied Mathematics.

This fact is due, on one hand, to the frequent use of Partial Differential Equations in the Physical, Technological, Economic, and other Applied Sciences, and on the other hand, to the multitude of new problems, questions, and theories that are created and developed in the area of Theoretical Mathematics from research efforts directed at solving and studying these equations more broadly.

The theory of Complex Functions, also known as Complex Analysis, is an important branch of Mathematics and particularly Mathematical Analysis, which studies the properties of functions of complex numbers. It is useful in many branches of Mathematics, such as Algebraic Geometry, Number Theory, and Applied Mathematics, as well as in Physics, including Hydrodynamics and Thermodynamics, String Theory, and Quantum Field Theory, but also in areas of Engineering, such as Aerospace, Mechanical, and Electrical Engineering.

Over the decades, it has emerged as one of the most beautiful and useful subjects in Mathematics. In modern times, it has gained popularity through a new impetus from Complex Dynamics and the images of fractals produced by iterating entire functions.