Textbook in PDF format This book provides an introduction to 3D rotations, laying the foundation for advanced topics by covering the fundamentals of rotations in three dimensions. No book on rotations currently provides a clear introduction, linking the disparate topics involved with beginning study on this subject. This book starts with the basics, including vector topics relating specifically to 3D finite rotations and progresses in a logical way to rotation matrices, axis/angle representation, Euler-Rodrigues rotation formula, Euler parameters (and quaternions) and Euler angles, providing the necessary linkage between these topics. The special orthogonal group and Euclidean group are introduced along with Chasles' theorem and the book concludes with concepts in infinitesimal rotations. This book uses 3D diagrams to aid understanding and visualization. This book is read by undergraduates, graduate students and those working in industry who find themselves encountering rotations for the first time and provides a clear path to be completed that places the reader in a strong position to navigate more complex material on the subject of rotations. Preface. Introduction to Rotations in Three Dimensions. Vectors. Rotation in Two Dimensions. Direction Cosine Matrix. Euler’s Rotation Theorem and Formula. Euler–Rodrigues Parameters. Rodrigues Method for Combining Rotations. Euler Angles. Groups. Rotation Group. Quaternions. Quaternions and Rotations. Angular Velocity. References. Appendix A Matrix Material. Appendix B Rodrigues Paper. Appendix C Euler Angles. Appendix D Groups. Appendix E Angular Velocity. Index