A Journey Around the Different Scales Involved in the Description of Matter and Complex Systems: A B

1 The Schrödinger equation.- 1.1 The history of quantum mechanics in small bits.- 1.2 Planck versus the ultraviolet catastrophe.- 1.3 An intuitive approach to the Schrödinger equation.- 1.4 The Feynman approach.- 1.5 The Schrödinger equation.- 1.6 Relations between position and momentum wavefunctions.- 1.7 Heisenberg uncertainty principle.- 1.8 Observable and its time evolution.- 1.9 The Hellmann-Feynman theorem.- 1.10 The Pauli exclusion principle.- 1.11 On the numerical solution of the Schrödinger equation.- 2 Ab-initio calculations.- 2.1 The Hartree-Fock description.- 2.2 Density Functional Theory.- 2.3 Concluding remarks on the quantum scale.- 3 Coarse-grained descriptions.- 3.1 Molecular dynamics.- 3.2 Brownian dynamics.- 4 Kinetic theory models. 4.1 Motivation.- 4.2 Kinetic theory description of simple liquids and gases.- 4.3 Complex fluids.- 4.4 The Chemical Master Equation.- References.