Parton Cascades, Small x, and Saturation in High Energy Collisions

Abstract: These lecture notes are a combination of two lectures and a contribution to the celebration of Andrzej Bia{\l}as' birthday at the LI Cracow School of Theoretical Physics in June 2011. I here discuss the dynamics of particle production in high energy reactions. It includes parton cascades and hadronization in e+e--ann., small x evolution including the Double Leading Log approximation and the BFKL equation, saturation at high densities and the BK equation, and finally the Lund Dipole Cascade model for high energy collisions, which is implemented in the DIPSY MC.