Delve into the intricacies of fractionalized metallic phases in the single band Hubbard model through this comprehensive lecture by Subir Sachdev. Explore key concepts such as the pseudogap regime, Fermi arcs, and the interplay between Fermi liquid and Z2 gauge theory. Gain insights into experimental evidence, photoemission spectra, and the challenges of modeling high-temperature superconductors. Engage with in-depth discussions on topics ranging from charge carrier density to random matrix models, and benefit from extensive Q&A sessions addressing complex queries from the audience. This advanced physics talk, part of a joint course with TIFR, IAS, and ICTS, offers a deep dive into quantum phases of matter and their implications for understanding exotic materials.