Geometry of the cutting tools is one of the crucial parameters affecting the quality of manufacturing processes. The geometry of the surface generated on the blank is dependent upon the geometry of the cutter. This book outlines in detail geometric models of single-point and multi-point cutting tools and proposes a set of new three-dimensional (3D) standards for defining the tool geometry. The 3D geometric models of cutting tools would help the design, analysis and manufacturing processes of the cutting tools. Relations are developed to map 3D angles to equivalent conventional angles as detailed in ASA, ORS and NRS standards. This set of relations is known as forward mapping. Similarly, the relations to find 3D angles from the given conventional angles, inverse mapping, are also established. The setting or swivel angles for grinding and their relations with 3D rotational angles are developed for single-point cutting tool to generate features for resharpening. To illustrate the utility of 3D definitions of cutting tools, a few case studies on Finite Element based Analysis, CNC machining and geometric assessment of tool wear and defects of different cutting tools are considered.