The book presents in an accessible form the main ideas and methods of dynamics of systems with one-way connections. The phenomenon of impact on the connection is considered from the point of view of general Lagrangian formalism. From the standpoint of a constructive approach, justification is made for various models of impact interaction. The existence and stability of periodic trajectories in impact systems are investigated. In the conservative case, variational principles and methods are widely used. A special place is occupied by research from the qualitative point of view of various billiard tasks. In particular, a wide range of integrable billiards (including multidimensional ones) is discussed, as well as results on the non-integrability of a typical billiard .. The book contains a historical outline of the development of the main ideas of the theory of impact. For specialists in the field of analytical mechanics and theory of dynamical systems; can be useful for students of mechanical and mathematical specialties .