This book offers a concise introduction to non-Fermi liquid (NFL) states—metallic systems that lie beyond the scope of Landau Fermi liquid theory. NFLs emerge in strongly interacting quantum many-body systems, where conventional quasiparticle descriptions fail due to coupling between soft Fermi surface fluctuations and gapless bosonic modes. These systems are governed by strongly coupled quantum field theories and are often linked to anomalous transport behavior in unconventional superconductors.The text presents analytic techniques, including dimensional regularization, for studying NFLs in a controlled framework. Topics include the Ising-nematic quantum critical point, superconducting instabilities enhanced by Ising-nematic fluctuations, NFL behaviour induced by transverse gauge fields, and the NFL induced by charge-density wave orderings. A basic background in quantum field theory is assumed.This volume is intended for graduate students and researchers in theoretical condensed matter physics, particularly those working on quantum criticality and emergent metallic phases.
