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. This course will discuss subjects at the frontier in condensed matter physics, where will be introduced both theoretical frameworks and experimental finding of emergent quantum phenomena, albeit with their current limitation. The latter will set an arena to construct a fruitful scientific discussion among students of this course making our class more dynamic and challenging while learning hot subjects in physics. As consequence, the student of this course will be capable to elaborate new paradigm on quantum matter recognized relevant degrees of freedoms as shown in the ecosystem of figure 1. Figure 1. Schematic representation of the syllabus structure constructed on relevant degrees of freedom of quantum matter, whose collective interaction are matter of scientific discussion in this course. This approach will bring to understand the relevance of Emergent Phenomena in Correlated Quantum Matter. Solid represent correlations while dashed lines and arrows represent the horizon that correlated quantum matter creates (Source: @JulioLarrea’s Authorship).