This book offers a compact tutorial on basic concepts and tools in quantum many-body physics
and focuses on the correlation effects produced by mutual interactions. The content is divided
into three parts the first of which introduces readers to perturbation theory. It begins with
the simplest examples-hydrogen and oxygen molecules-based on their effective Hamiltonians and
looks into basic properties of electrons in solids from the perspective of localized and
itinerant limits. Readers will also learn about basic theoretical methods such as the linear
response theory and Green functions. The second part focuses on mean-field theory for itinerant
electrons e.g. the Fermi liquid theory and superconductivity. Coulomb repulsion among
electrons is addressed in the context of high-Tc superconductivity in cuprates and iron
pnictides. A recent discovery concerning hydride superconductors is also briefly reviewed. In
turn the third part highlights quantum fluctuation effects beyond the mean-field picture.
Discussing the dramatic renormalization effect in the Kondo physics it provides a clear
understanding of nonperturbative interaction effects. Further it introduces readers to
fractionally charged quasi-particles in one and two dimensions. The last chapter addresses the
dynamical mean field theory (DMFT). The book is based on the author's long years of experience
as a lecturer and researcher. It also includes reviews of recent focus topics in condensed
matter physics enabling readers to not only grasp conventional condensed matter theories but
also to catch up on the latest developments in the field.
