Explore the foundations and historical development of topology in this comprehensive 56-minute lecture. Delve into Euler's groundbreaking work on polyhedron characteristics and Descartes' early insights into curvature analysis. Examine Poincaré's contributions to understanding topological invariance and the concept of rational turn angles. Investigate Riemann's influential work on complex functions and surfaces, leading to the classification of two-dimensional surfaces. Learn about key concepts such as the Euler characteristic, homeomorphisms, and simply connected spaces. Gain insights into the Poincaré conjecture and its recent resolution. Suitable for those interested in the historical evolution of mathematical ideas and the fundamental principles of topology.