This course draws a connection between the microscopically deterministic and/or chaotic dynamics of complex systems and their macroscopic appearance. It illustrates how complex structures and dynamics arise from the compound effect of simple rules of evolution in time, laying the foundations of statistical equilibrium and equilibrium thermodynamics. Equilibrium thermodynamic describes one extreme limit of multi-dimensional systems in chaotic motion. It derives and utilizes phenomenological relations between a few salient macroscopic system parameters, which depend simultaneously on the inherent structure and the energy content of the system.

The different phases of matter (gases, liquids, solid) assumed by bulk classical interacting particles and their transitions are discussed in this approximation. Properties of non-interacting quantal systems are expressed in terms of partition functions, for gases of simple and complex particles. Non-equilibrium statistical behavior of multi-particle systems leads to diffusion and other transport phenomena. Finally, the macroscopic time evolution of complex systems is described in terms of Statistical Transport Theory. It explains how system response to the local environment leads to an approach of its global equilibrium.