The theory of quadratic number fields is the first step towards a general theory of algebraic number fields. In this book, the main theorems of the theory are not proven in the shortest way; rather, we take the time to familiarize ourselves with the new objects through small detours and illustrate the theorems with many examples. Additionally, we delve into the history of algebraic number theory and discuss some important examples for the development of this discipline. Diophantine equations, in particular, play a significant role. The book is complemented by numerous exercises and a brief introduction to calculations with Pari and Sage.