Robotics is commonly defined as the science studying the intelligent connection between perception and action. As such, the full scope of robotics lies at the intersection of mechanics, electronics, signal processing, control engineering, computing and mathematical modelling. Within this very broad framework, modelling and control play a basic role, not only in the traditional context of industrial robotics, but also for the advanced scenarios of field and service robots, which have attracted an increasing interest from the research community in the last twenty years. Robot modelling and control are dealt within this course. Kinematic models of both robot manipulators and mobile robots are presented. The Jacobian is introduced as the fundamental tool to describe differential kinematics, determine singular configurations, analyze redundancy, derive the statics model and formulate inverse kinematics algorithms. The equations of motion of a robotic system are found on the basis of the dynamic model which is useful for motion simulation and control algorithm synthesis. Model-based control offers the best performance for tracking motion trajectories suitably planned in either joint or operational space. Controlling the interaction of a robot with the environment requires the adoption of force control and/or visual control. All such control techniques rely on effective parameter estimation methods. On the other hand, for mobile robots trajectory planning methods have to properly account for the nonholonomic constraints, and the motion control problem is tackled with reference to two tasks: trajectory tracking and posture regulation.