This book is a wide-ranging survey of the physics of out-of-equilibrium systems of correlated electrons, ranging from the theoretical, to the numerical, computational and experimental aspects. It starts from basic approaches to non-equilibrium physics, such as the mean-field approach, then proceeds to more advanced methods, such as dynamical mean-field theory and master equation approaches. Lastly, it offers a comprehensive overview of the latest advances in experimental investigations of complex quantum materials by means of ultrafast spectroscopy.

Ferdinando Mancini is Professor Emeritus of Structure of Matter of the Department of Physics, University of Salerno (Italy), and President of the International Institute for Advanced Scientific Studies. During his very long career he has accumulated professional experience in Quantum Field Theory, Statistical Mechanics and Condensed Matter Physics focusing on Highly Correlated Systems, Superconductivity, Ferromagnetism and Heavy-Fermion Systems.

Dr. Roberta Citro is an Associate Professor in Theoretical Physics at the Department of Physics of the University of Salerno (Italy). In recent years she has gathered professional experience in many-body techniques of low-dimensional systems and in quantum transport in nanostructures. She has extensive experience in the field of cold atoms systems, working on the problem of non-equilibrium dynamics of a Bose gas subjected to a time-dependent perturbation. She is an active member of the organizing committees of different internationalconferences, referee of APS, IOP and Nature Physics journals and deputy editor of EPL. She received the Italian Physical Society Award (1998) and a Fulbright Award (1999).

Master equation versus Keldysh Green's functions for correlated quantum systems out of equilibrium.- Towards an understanding of superconductors and correlated materials out-of-equilibrium: mean-field approaches.- Electronic structure of correlated materials out of equilibrium: non-equilibrium dynamical mean-field theory.- Ultrafast optical control of complex quantum materials.