The book comprises three closely related parts: the first is devoted mainly to curve and surface modeling, and contains one general survey on theoretical and practical applications of algebraic methods and three specialized surveys on surface blending, parametrization, and implicitization, followed by four research papers. The second part is concentrated on geometric reasoning, with one tutorial survey on Clifford algebra approaches, another on automated deduction in real geometry, and one research article. The last part is highlighted by a chapter that outlines a theory of real approximation, based on a generalization of the central idea of exact geometric computation. The book ends with one paper on A-resultant quotients and another on face recognition, which show how computer algebra and artificial intelligence meet geometry in the era of computation.