This book is a graduate-level text in which 3X3 coordinate-transformation matrices and 3-element vectors with dual-number elements are used to analyze the mechanics of mechanisms, robots and other mechanical systems. The use of dual numbers allows a very compact and convenient notation for the analysis of displacements, velocities, static equilibrium and dynamic equilibrium. The concept of the dual number has been around since the 19th century but has not become popular because there has not been a textbook available to facilitate learning the concepts and methods. Mention of the dual number and its applications have been more frequent in recent years but have been scattered about in journal articles with varying approaches and notation. This text features a well organized explanation of how the dual-number can be applied with examples and exercises so that the reader can use dual-number methods to analyze mechanical systems of interest.