Abstract: This talk concerns mathematical theory of the so-called Fluctuation Relation (FR) and Fluctuation Theorem (FT) in context of dynamical systems relevant to physics. The FR refers to a certain universal identity linked to statistics of entropy production generated by a reversal operation and FT to the related mathematical large deviations result. The discovery of FR goes back to numerical experiments and Evans, Cohen and Morris (1993) and theoretical works of Evans and Searles (1994), Gallavotti and Cohen (1995). These discoveries generated an enormous body of numerical, theoretical and experimental works which have fundamentally altered our understanding of non-equilibrium physics, with applications extending to chemistry and biology. In this talk I will introduce modern theory of FR and FT on an example and comment on a current research program on this topic.