Dive into the first lecture of the Machine Learning the Landscape series, delivered by Yang-Hui He at the Kavli Asian Winter School on Strings, Particles and Cosmology. Explore fundamental concepts in mathematics and string theory, including Riemann surfaces, cohomology, Calabi-Yau manifolds, and string phenomenology. Learn about heterotic compactification, special holonomy, and topological properties of Calabi-Yau manifolds. Discover explicit examples of these complex geometric structures and their applications in theoretical physics. Engage with cutting-edge topics such as cyclic manifolds, triadophilia, and Complete Intersection Calabi-Yau (CICY) 3-folds. Conclude with a Q&A session to deepen your understanding of these advanced concepts in high-energy theory and mathematical physics.