Computer Graphics continues to battle the challenging question: “How quickly and effectively can a designer transform a mental concept into a digital shape, which is easy to refine and reuse?” Traditional techniques of sculpting and sketching continue to be among the quickest and most expressive ways for designers to visually manifest their ideas. This course traces the evolution of interactive shape design from traditional media to the state of the art in digital modeling techniques, both in commercial software and academic research. The course will cover the gamut of hardware devices and interaction paradigms used in digital modeling and their underlying mathematical representations of shape. The audience will be presented with the properties of various implicit, explicit and hybrid shape representations and the capabilities, limitations and implementation details of current algorithms for interactive shape creation and manipulation. The goal of this course is to impart the audience with both an understanding of the big open questions as well as the skills to engineer recent research in interactive shape modeling applications.