In this chapter, we consider the motion of a rigid body when a particular point in space is fixed. Sometimes, this fixed point is taken to be the center of mass of the body, and the problem becomes relevant for the computation of the dynamics of satellites. When the fixed point is not taken to be the center of mass, and gravity is acting on the system, the problem becomes relevant for describing the dynamics of heavy tops. In this chapter, we will first develop the general formalism of rotation matrices necessary to describe the system. We then derive equations of motion for the rigid body with and without the external torques and compute several conserved quantities. We then consider the question of the heavy top, discuss the integrability of several cases (Euler, Lagrange, and Kovalevskaya), and derive the complete solution of the Lagrange top.