Historically, the evaluation of the “dexterity” of a given manipulator has been presented as a difficult qualitative and context-dependent task. The nature of this task has given rise to numerous definitions for quantitative properties associated with a manipulator, all referred to as dexterity. By divorcing the kernel of the idea of dexterity from the qualitative evaluation, a novel, unified, and simple definition for manipulator dexterity has been developed. The new definition of dexterity retains the spirit of all previous definitions. Simplicity is retained by recognizing that all velocity analyses and hence all measures of dexterity are governed by linear systems of algebraic equations. The derivations presented are general and may be universally applied to both redundant architectures and non-spanning substructures.