The main goal of this course is to bring the audience a discussion of the state-of-the-art of novel and exotic quantum phenomena which emerge from strong correlation between different degrees of freedom of electron (spin, orbital, charge) and low-lying excitation modes (phonons, magnons, polarons, etc). The discussion will focus on some relevant cases, where degrees of freedom collectively mediated by low-energy scales interaction bring to new states of matter, remarkably different from those states in non-interacting system. Such novel quantum states and phases bring a new definition of Quantum Matter, whose comprehension is promising for the realization of a new generation of materials with potential for high-tech application.