This book provides a comprehensive introduction to the modeling, analysis, and simulation of mechanical systems with frictional contact, making it suitable for classroom instruction, workshops, and independent study. It introduces the fundamental challenges posed by frictional and unilateral constraints, explains why nonsmooth dynamics is needed to describe such systems, and presents the key modeling and simulation approaches used in the field. The book develops the necessary mathematical foundations in convex analysis before building a rigorous framework for force laws expressed through set-valued relationships, including friction and impact laws. It then applies these concepts to dynamical systems with nonsmooth interactions, equipping readers with both the theoretical understanding and practical skills needed to analyze and simulate mechanical systems with frictional contact, including the use and further development of MATLAB-based simulation tools.