Explore emergent phenomena in strongly correlated quantum systems through this 53-minute lecture delivered by Thereza Paiva from UFRJ, Brazil, as part of the II School on Emergent Phenomena in Non-Equilibrium Quantum Many-Body Systems. Delve into the complex behaviors that arise when quantum particles interact strongly with each other, leading to collective phenomena that cannot be understood from the properties of individual particles alone. Learn about the theoretical frameworks and computational methods used to study these systems, including how strong correlations give rise to novel phases of matter and unexpected physical properties. Examine specific examples of strongly correlated materials and their applications in condensed matter physics. Gain insights into the mathematical tools and conceptual approaches needed to understand how microscopic interactions lead to macroscopic emergent behaviors in quantum many-body systems.