The book is a comprehensive account of orientations and rotations of three-dimensional objects. The author's interest in orientations stems from the field of crystallographic texture analysis - a branch of knowledge concerned with orientations of crystallites constituting polycrystalline materials. Essentially, Orientations and Rotations treats the mathematical and computational foundations of texture analysis. It contains an extensive and thorough introduction to parameterizations and geometry of the rotation space. Since the notions of orientations and rotations are of primary importance for science and engineering, the book can be useful for a very broad audience using rotations in other fields (robotic manipulators, spacecraft control, computer animation, limb or eye kinematics, etc.).