In this chapter we will describe the motion of mass points in space and time and their trajectories by vectors \({\vec r}(t)\) , \({\vec v}(t)\) and \({\vec a}(t)\) . The mathematical tools are differentiation in cartesian or polar coordinate systems of a three-dimensional real vector space, which is used to uniquely define physical quantities like inertial systems, velocity, acceleration, angular velocity or angular acceleration. A brief introduction to Euclidean vector spaces will been given and linear transformations (like rotations) be described by suitable 3 \(\times \) 3 matrices. This allows for a rigid formulation of kinematics also in case of circular motion.