Explore advanced concepts in chiral Luttinger liquid theory through this second lecture in a two-part series delivered by Prof. Biao Lian from Princeton University. Delve into the complex interactions and various phases that emerge within chiral Luttinger liquid systems, building upon foundational concepts from the first lecture. Examine the theoretical framework governing these one-dimensional quantum many-body systems where particles exhibit chiral behavior, and analyze how interactions between particles lead to different quantum phases of matter. Learn about the mathematical formalism used to describe these systems and understand the physical implications of chirality in condensed matter physics. This lecture forms part of the Princeton Summer School for Condensed Matter Physics (PSSCMP), providing graduate-level instruction in cutting-edge topics in theoretical condensed matter physics.