This learning and reading book provides an introductory overview of the fundamental methods and results of algebra. As is common in introductory lectures, it consists of three parts: groups, rings, and fields, which are the foundational pillars of algebra. The highlight of the third chapter is the classical Galois theory presented in a contemporary format, where many of the previously achieved results are integrated. In addition to the usual content, the book also includes excursions into advanced topics, such as symmetries of Platonic solids, quadratic number rings, or root expressions for unity roots using Gauss's method. A detailed appendix describes the development of the axiomatic method from Euclid to Bourbaki. To gently familiarize students of algebra with the subtle methods and the intricate web of concepts, many motivating introductory remarks are provided.