This chapter discusses the dynamics of mechanical systems with a finite number of degrees of freedom, focusing on unilateral constraints and dry friction. The author, Jean Jacques Moreau, develops an approach that does not assume convexity in the constraint inequalities and allows for non-differentiable velocity functions. The velocity is defined as the time integral of a velocity function with locally bounded variation, and the acceleration is represented by a measure on the time interval. The dynamics are governed by measure differential inclusions, which handle velocity jumps and collisions as soft, dissipative events. The friction is modeled using a recently proposed expression of Coulomb's law. These formulations are advantageous for generating numerical algorithms that can handle the nonsmooth effects arising from unilateral constraints and dry friction. The chapter also covers the kinematics, Lagrange equations, and the dynamics of smooth frictionless motions, providing a detailed mathematical framework for understanding and simulating such systems.This chapter discusses the dynamics of mechanical systems with a finite number of degrees of freedom, focusing on unilateral constraints and dry friction. The author, Jean Jacques Moreau, develops an approach that does not assume convexity in the constraint inequalities and allows for non-differentiable velocity functions. The velocity is defined as the time integral of a velocity function with locally bounded variation, and the acceleration is represented by a measure on the time interval. The dynamics are governed by measure differential inclusions, which handle velocity jumps and collisions as soft, dissipative events. The friction is modeled using a recently proposed expression of Coulomb's law. These formulations are advantageous for generating numerical algorithms that can handle the nonsmooth effects arising from unilateral constraints and dry friction. The chapter also covers the kinematics, Lagrange equations, and the dynamics of smooth frictionless motions, providing a detailed mathematical framework for understanding and simulating such systems.