This book aims to foster a deep and lasting understanding of mathematical ideas by emphasizing intuition, connections, and problem solving rather than rote computation. Above all, it seeks to build confidence in exploring, questioning, and understanding mathematics. Prepared to accompany my lectures, this notebook is a working document rather than a traditional textbook. Its concise format leaves space after each topic for notes, questions, and assigned work, encouraging active engagement and organized thinking. In line with contemporary mathematical practice, it integrates modern technology, including AI-based learning tools such as symbolic algebra systems, graphing and visualization engines, numerical solvers, and AI tutors that can answer questions, generate examples, test conjectures, and offer alternative explanations. Used thoughtfully, these tools function much like a personal tutor—enhancing learning without replacing rigor or human judgment. Finally, this notebook is a work in progress. It reflects ongoing efforts to refine ideas, develop original problems, and introduce real-world applications. I hope it supports you not only in following the course, but also in cultivating a confident, organized, and creative approach to mathematics.