This is an introduction to the mathematical theory of Lie groups. About the first half of the book deals with matrix groups. Abstract concepts (including manifolds) are introduced only in the second half. To provide motivation and a better historical understanding, short texts by classical authors (such as Sophus Lie himself) are interwoven throughout. Additionally, there is a dedicated chapter that exclusively discusses various geometric transformation groups, specifically addressing classical geometries. Only the usual study content from the first year of a mathematics or physics degree is required as prior knowledge, particularly concerning analysis and linear algebra. The book starts at a very elementary level. Everything else is not only introduced but all theorems are also proven. Emphasis is placed on clarity and comprehensibility.