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Affine algebra has developed in many directions since its inception. This often poses a problem for undergraduate/graduate/research students-which direction should one follow? What do these ideas have to do with robotics? This book offers a more focused treatment of the applications of algebraic properties in robotics. This is designed to make robotic algebra an approachable and interesting subject for the readers, especially students, researchers in robotics. The authors consider the development of theory in affine algebra in the context of application towards robot motion planning. The main theorems on verities and polynomials are presented with the proofs. The authors then introduce the methods of algebra with some notions from topology and develop them towards the goal of constructing robot models with joints. Interesting diversions are offered such as snake joints and snaky arms. This monograph is presented in its simplest form with short necessary details. The theoretical and practical importance of the abstract concepts is briefed, which will help the students familiarize themselves with the topic.