This book is a collection of problems for Gamma functions and Riemann zeta functions, which are special functions that occupy an important place in the field of mathematics and engineering. In this book, we will present the readers with the characteristics of the Gamma and the Riemann zeta function and the skillful mathematical skills and the related problem solving techniques. In this book, we will focus on the open problems presented by several mathematicians. We first address the issues that are the starting points for open problems, and then consider these problems. d to help students to study the subject. These problems will be a good task for students who are learning or majoring in mathematics, and in the process they can have a lot of experience and a high degree of mathematical ability.