Our project has a twofold purpose: firstly it aims at a better understanding of fundamental properties of classical and quantum dynamical systems, with a particular prominence on unconventional transport and dynamical features (fractal spectra, weak chaos, infinite ergodic theory, almost resonant quantum systems). Secondly it addresses features that characterize the behavior of many particle systems, with a methodology that takes into account the former dynamical perspective: examples include normal and anomalous heat conduction in long chains, equilibrium and non equilibrium aspects of systems with long range interactions - with an emphasis on self-gravitating systems-, coherent transport in light harvesting systems, and statistical analysis of social and economic systems.