This PDF is a visually guided introduction to the foundational concepts of topology. It is aimed at helping you develop an intuitive and rigorous understanding of topological spaces. We will look at key topics such as open sets, quotient topologies, and classic constructions like the torus, Möbius strip, Klein bottle, and real projective plane, both from the intuitive point of view and rigor with practice. But most importantly, we will answer the question: "How does the concept of open sets relates to these topological shapes?". This work will systematically build your understanding, beginning with basic definitions and progressing to more advanced notions involving topological identification via equivalence relations. It follows our DIBEOS METHOD: 1. Intuition, 2. Concrete examples, 3. Rigor, 4. Practice (exercises). Enjoy, and thank you for supporting our work!