  In these lecture notes we review some recent attempts at searching for
non-Fermi liquids and novel quantum phase transitions in holographic systems
using gauge/gravity duality. We do this by studying the simplest finite density
system arising from the duality, obtained by turning on a nonzero chemical
potential for a U(1) global symmetry of a CFT, and described on the gravity
side by a charged black hole. We address the following questions of such a
finite density system:
  1. Does the system have a Fermi surface? What are the properties of low
energy excitations near the Fermi surface?
  2. Does the system have an instability to condensation of scalar operators?
What is the critical behavior near the corresponding quantum critical point?
  We find interesting parallels with those of high T_c cuprates and heavy
electron systems. Playing a crucial role in our discussion is a universal
intermediate-energy phase, called a "semi-local quantum liquid", which
underlies the non-Fermi liquid and novel quantum critical behavior of a system.
It also provides a novel mechanism for the emergence of lower energy states
such as a Fermi liquid or a superconductor.

High Energy Physics - Theory;Strongly Correlated Electrons