QCD critical point and hydrodynamic fluctuations in relativistic fluids

These lecture notes consist of two major connected parts. The first part (Sections 1, 2), after a brief historical introduction, deals with the physics of critical points in thermodynamic equilibrium. The features of the fluctuations relevant for the QCD critical point search are highlighted. The second part (Sections 3, 4) focuses on the recent developments in the description of the fluctuation dynamics especially relevant for the QCD critical point search in heavy-ion collisions.