Introduction.- The Theory: Mechanics An example: Collision of a Point and a Plane.- The Theory: Mechanics and Thermics An Example: Collision of two Balls.- Collisions of Rigid Solids: Three Disks in a Plane.- Collisions of Rigid Solids: Three Balls in a Box.- Pedestrian Trajectories and Collisions in Crowd Motion.- Collisions of Deformable Solids. Collisions of Rigid Solids and Fluids.- Debris Flows and Collisions of Fluids and Deformable Solids.- Shape Memory Alloys and Collisions.- Conclusion.- Some Elements of Convex Analysis.