The goal of the book "Mathematics: A Concise Introduction" is to explain, carefully but in a non-technical level, the differences between advanced research-level mathematics and the type of mathematics we learn in school. In this context, some important, seemingly paradoxical concepts such as infinity, imaginary numbers, and curved space are presented and explained. The first chapters deal with general aspects of mathematical thinking, while those that follow address more specific issues, such as limits and infinity, dimension, geometry, estimations, and approximations. The book concludes with answers to some common sociological questions about the mathematics community.