This text introduces a rapidly growing new research area - the study of dynamical properties of elementary fields. The methods used in this field range from algebraic topology to parallel computer programming. The main aim of this research is to understand the behaviour of elementary particles and fields under extreme circumstances, first of all at high temperature and energy density generated in the largest accelerators of the world and supposed to be present in the early evolution of our universe shortly after the Big Bang. In particular, chaos is rediscovered in a new appearance in these...