Understanding Rheology is a main text for advanced undergraduate or graduate level courses taught in departments of chemical and mechanical engineering. Rheology is the study of the deformation and flow of materials. The plastic flow solids, such as molten rock, and the physical properties of complex fluids such as polymers, colloids, foams, gels are among the chief concerns of rheology. The field of rheology is an industrially important one, and one that is growing rapidly. Rheology is of primary importance in polymer processing, food processing, coating and printing, and many other manufacturing processes. This text begins with refresher sections on tensor and vector operations and Newtonian fluid mechanics which the students may or may not have retained from their fluid mechanis course (a certain prerequesite to this course), but which are essential to comprehending the material in this subject. Each chapter contains a problem set designed to reinforce materal covered in the chapter. The problems, samples, and mathematics in this text are appropriate to an undergraduate readership. This book also contains discussion of current jobs such as birefringence and the modern state of optics in measuring rheological phenomena. This text is also designed for practicing engineers and scientists to use as a self-teaching guide to those rheological principles they find applicable to their work. The text contains example problems that will allow the reader to practice the subject under discussion. The appendices in this text contain reference material which should be of interest to this audience.