This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects. It is designed as a bridge between elementary courses in analysis and linear algebra and more advanced classes in algebraic and geometric topology, making it particularly suitable for both undergraduate and graduate mathematics students. Additionally, it can be used for self-study.The authors employ the modern language of category theory to unify and clarify the concepts presented, with definitions supported by numerous examples and illustrations. The book includes over 170 exercises that reinforce and deepen the understanding of the material.