This textbook provides a comprehensive and rigorous introduction to various mathematical topics that play a key role in economics and finance. Motivated by economic applications, the authors introduce students to key mathematical ideas through an economic viewpoint, starting from the real line and moving to n-dimensional spaces, with a special emphasis on global optimization. Additionally, the text helps unacquainted, but intellectually curious, students become familiar with mathematical proofs. The book is suitable for both self-study and rigorous introductory mathematics courses for undergraduate students majoring in economics or finance.