These lectures will report on Correlated Basis Function Theory and its applications to strongly interacting homogeneous systems. Fermi Hypernetted Chain (FHNC) will be discussed in detail and presented as a method to compute two- and three-body distribution functions and the one-body density matrix for trial wave function of the Feenberg-type. Applications to liquid helium, nuclear matter and strongly correlated electron systems will also be presented.
Correlated Basis Function Theory will be developed with the perspective of going beyond variational theory for strongly correlated Fermi systems. Applications to the optical potential and the momentum distribution of nuclear matter will be discussed.
Finally, a new FHNC scheme to deal with spin-dependent correlations will be presented. Such a scheme is based upon the spin-coherent representation of the spin-dependent correlations, and solves the problem of the commutator terms arising in standard FHNC/SOC theory.