of classical screw theory accessible to a more general audience arrived in the early 1980’s, when Roger Brockett showed how to mathematically describe kinematic chains in terms of the Lie group structure of the rigid-body motions [20]. This discovery allowed one, among other things, to re-invent screw theory simply by appealing to basic linear algebra and linear deferential equations. With this “modern screw theory” the powerful tools of modern di↵erential geometry can be brought to bear on a wide-ranging collection of robotics problems, some of which we explore here, others of which are covered in the excellent but more advanced graduate textbook by Murray, Li and Sastry [122]. As the title indicates, this book covers what we feel to be the fundamentals of robot mechanics, together with the basics of planning and control. A thorough treatment of all the chapters would likely take two semesters, particularly when coupled with programming assignments or experiments with robots. The contents of Chapters 2-6 constitute the minimum essentials, and these topics should probably be covered in sequence.