Critical phenomena and scale invariance -- Invariance properties of the renormalization group -- Scale transformations in dynamic models -- Critical dynamics in fokker-planck formalism -- Dynamic critical phenomena and the renormalization group — Application to a Lattice dynamic model -- The algebraic approach.to quantum statistical mechanics. Equilibrium states and hierarchy of stability -- Theorems on phase transitions with a treatment for the Ising model -- Statistical mechanics of equilibrium systems: Some rigorous results -- Probabilistic aspects of critical fluctuations -- The application of renormalization group techniques to quarks and strings -- The role of spontaneous broken symmetry.