The second edition is still unique in providing a deep understanding of the subject: rather than focusing on the calculation results in kinematics and robotics, it includes a significant state-of-art that reflects important advances in the field, robotics links back to the fundamental mathematics of group theory and geometry. Main features: * Beginning with a brief survey of basic ideas in algebra and differential geometry, Lie groups and Lie algebra * Examine how, in a new chapter, Clifford algebra that are relevant to the robot kinematics and Euclidean geometry in 3D * Introduce math concepts and methods using examples from robotics * Solve substantial problems in the design and control the robot via a new method * Provide solutions to problems enumeratif famous robot kinematics using intersection theory on the group of rigid body motion * Extend the dynamic, in another new chapter, for the robot with the end-effector constraints, which lead to the equations of motion for a parallel manipulator The basics of the geometry of the Robotics serve a broad audience of graduate students and researchers in various fields, particularly mechanical engineering, computer science, and applied mathematics.