This monograph provides a detailed record of the "e;GRUFF"e; research project. The goal of the GRUFF project is to develop techniques for robotic vision systems to recognize objects by reasoning about their intended function rather than matching to a pre-defined database of 2-D object appearances or 3-D object shapes. The contributions of this work are: a demonstration of the feasibility of the "e;form and function"e; approach to reasoning about 3-D shapes; a demonstration of the concept of using a small number of knowledge primitives as component building blocks in creating a function-based definition of an object category; and an indexing mechanism to make processing for recognition more efficient without any substantial decrease in correctness of classification. Results are given for the analysis of over 500 3-D shape descriptions created with a solid modeling tool and over 200 shape descriptions extracted from real laser range finder images.