This book is an appropriate reference book intended for not only professional mathematicians but also aspirant readers who are eager to have basic knowledge of mathematical constants and special functions. Especially, for students and scholars who have interests in mathematical constants and special functions, this book is so inspiring and encouraging.Since the theory of constants and special functions has grown enormously, the present book reflects only one of the remarkable parts. In other words, we paid special attention to find out better approximation formulas and related inequalities.This book will help students and scholars to understand constants and special functions such as the Euler's constant and the gamma function and learn how to find new approximation formulas and related inequalities.We believe that this book will be fundamental reference in the constant and special function field and our results can be used to bring about another development in this field.At the end, we'd like to take this opportunity and give sincere thanks to all contributing authors, referees, in making this book a worthy tribute to readers.