Final Activity Report Summary - ULTRACOLD COLLISIONS (Molecular collisions in ultracold trapped gases) In this project we investigated molecular collisions in a gas at extremely low temperatures. Under such conditions even extremely weak forces, known as spin interactions, have a dramatic influence on the particles' dynamics. We developed theoretical methods necessary to describe very accurately this kind of phenomena and developed the corresponding computer programmes to perform quantitative calculations. We showed that, for many systems of main experimental interest, i.e. the alkali metal systems, the collision could not be efficiently manipulated by static external field. However, regular structures formed at the intersection of laser beams could be designed in order to control the molecular dynamics on a microscopic level. This was a result of major fundamental and applicative interest. A different numerical approach had to be developed for the study of more exotic atom-molecule systems, in which the molecule had an extremely large size. The method was based on the large velocity difference between the region of close approach of atom and molecule and the region on which the collision partners were far apart and only exerted a weak mutual influence. This approach was used for one-dimensional systems and it should be possible to extend it to higher dimensionality. Finally, we also provided theoretical data to interpret experiments performed with very cold atoms as they were associated into molecules by a magnetic field, developing extremely accurate collision models.