This course covers topics providing a window on quantum statistical mechanics with flush-backs to the classical case and links with quantum information theory, including q-bit based quantum formalism, quantum entropy, phase transitions and symmetry breaking, links between ground states of extensive quantum spin systems and thermal states of classical systems in (D+1) dimensions, few exact results for solvable quantum one dimensional systems (related to classical 2D systems), applicable analysis based in inequalities, links to stochastic geometric phenomena of percolation, random clusters, and loop soup models, and quantum entanglement.