  Instantons generate strong non-perturbative interactions between quarks. In
the vacuum, these interactions lead to chiral symmetry breaking and generate
constituent quark masses on the order of 300-400 MeV. The observation that the
same forces also provide attraction in the scalar diquark channel leads to the
prediction that cold quark matter is a color superconductor, with gaps as large
as $\sim$~100 MeV. We provide a systematic treatment of color superconductivity
in the instanton model. We show that the structure of the superconductor
depends on the number of flavors. In the case of two flavors, we verify the
standard scenario and provide an improved calculation of the mass gap. For
three flavors, we show that the ground state is color-flavor locked and
calculate the chiral condensate in the high density phase. We show that as a
function of the strange quark mass, there is a sharp transition between the two
phases. Finally, we go beyond the mean field approximation and investigate the
role of instanton-anti-instanton molecules, which -- besides superconducting
gap formation -- provide a competitive mechanism for chiral restoration at
finite density.
