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.