This book reviews the fundamentals of screw theory concerned with velocity analysis of rigid-bodies, confirmed with detailed and explicit proofs. The author additionally investigates acceleration, jerk, and hyper-jerk analyses of rigid-bodies following the trend of the velocity analysis. With the material provided in this book, readers can extend the theory of screws into the kinematics of optional order of rigid-bodies. Illustrative examples and exercises to reinforce learning are provided. Of particular note, the kinematics of emblematic parallel manipulators, such as the Delta robot as well as the original Gough and Stewart platforms are revisited applying, in addition to the theory of screws, new methods devoted to simplify the corresponding forward-displacement analysis, a challenging task for most parallel manipulators. Stands as the only book devoted to the acceleration, jerk and hyper-jerk (snap) analyses of rigid-body by means of screw theory; Provides new strategies to simplify the forward kinematics of parallel manipulators that can be easily implemented by non-experts in robot kinematics; Provides readers the opportunity to extend the theory of screws into the desired order of kinematic analysis in approaching open problems, e.g. the correct characterization of singularities in closed kinematic chains; Includes numerous end of chapter problems and solutions to illustrate concepts presented.