In this book, we are going to consider the elegant problems showing the relationships between the mathematical constants along with their solutions. The mathematical constants we are going to consider in this book include not only the well-known constants such as ln2, Pi, Napier's constant, Euler's constant, also various constants such as Riemann zeta function and Polylogarithm function coming out frequently in mathematical analysis.This book contains the open problems presented in several mathematical reference books and detailed solution of challenging problems, and also their new generalization problems. The problems and solutions presented here will attract interests of students and scientists who learn mathematics and engineering and will be helpful in some way in developing the theory of special function.We hope this book to be necessary for the mathematicians and students who are interested in solving mathematical problems and try to do new and amazing discovery in several fields of mathematics.