Explore the foundations of affine and projective geometry in this introductory lecture on Curves and Surfaces. Delve into basic notation and terminology for affine and projective points, associated vector spaces, and the use of projective coordinates to solve 2D geometry problems. Examine H. Grassmann's concepts in the context of products of projective row and column points. Gain insights into lines in 2D and 3D geometry, and discover the projective representation of curves. Learn about column K-vectors, affine grid planes, projective points equality, and the projective plane. Apply these concepts to solve 2D problems and understand projective curves in this comprehensive overview of geometric principles.