This course is concerned with fundamental concepts of geometric modeling. Geometric modeling combines approaches from numerical analysis, approximation theory, and differential geometry for the effective representation and manipulation of curves and surfaces. Specifically, this course introduces essential ideas based on data interpolation and approximation, Bezier curves, spline schemes, and a variety of algorithms related to these topics. This material should be of relevance to students with interest in the underlying mathematical and algorithmic foundation of modern computer-aided design (CAD) software systems.