The book is about mathematical and computational foundations of texture analysis. Numerical techniques are indispensable in texture analysis, so the book is primarily addressed to researchers and students using these techniques in practice. Orientations and Rotations is very different from other books on textures in its content and focal point. Major part of the book is devoted to orientations and rotations in general. Opening chapters contain an extensive and thorough introduction to rotations in three dimensions (including parameterizations and geometry of the rotation space). Further chapters are also general but they will be of interest for readers dealing with orientations of symmetric objects. This subject is essential for crystallographic textures since most crystal structures are symmetric. The final chapters concern more practical aspects of textures (such as the determination of orientations from diffraction patterns and the calculation of effective elastic properties of polycrystals). The book will be of interest for scientists working on plasticity, grain boundaries, recrystallisation, grain growth, and numerous other issues in which textures must be taken into account. Because of the extensive parts on rotations in general, the book can be valuable for everyone dealing with rotations.