1) Historical introduction to the investigation of Complex Systems.
2) Deepened analysis of the II Law of Thermodynamics to explain the natural irreversibility that every Complex System shows.
3) Complex Systems are out-of-equilibrium thermodynamic systems. Principles of Non-equilibrium Thermodynamics. Flows and Forces. Linear and Non-Linear regimes. Entropy Production and evolution criteria for the out-of-equilibrium systems.
4) Complex Systems exhibit non-linear dynamics. Therefore, it is mandatory to know the linear analysis of the stability of the stationary states: stable and unstable stationary states and oscillations. This analysis allows making predictions as far as the dynamical behavior of Complex Systems is concerned.
5) Oscillatory bio-chemical reactions, chemical waves, Turing structures. Periodic Precipitations. Relevance of these phenomena in nature.
6) Bifurcations and deterministic Chaos.
7) Fractal structures.
8) Natural and Computational Complexities. Strategies to promote worldwide sustainable growth and face the global challenges of this century.