Explore the theoretical framework of fractionalized Fermi liquids in this advanced physics lecture delivered at the Boulder Summer School 2025. Delve into the complex quantum many-body systems where conventional Fermi liquid theory breaks down, examining how fractionalization emerges in strongly correlated electron systems. Learn about the theoretical foundations that describe these exotic quantum states of matter, including the interplay between charge and spin degrees of freedom in systems where electrons appear to split into separate excitations. Investigate the mathematical formalism used to characterize these non-conventional metallic phases and understand their experimental signatures in condensed matter systems. Gain insights into cutting-edge research in quantum many-body physics and the theoretical tools needed to analyze strongly correlated materials that exhibit fractionalized behavior.