This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic diophantine equations. The first topic is further divided into two types of theories: classification over an algebraic number field and classification over the ring of algebraic integers. To ensure the book would be concise, the author proved basic theorems in local class field theory only in some special cases, and the Hilbert reciprocity law only over the rational number field. However, the author stated the main theorems with an arbitrary number field as the base field, so the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.