  We here classify of all the fully gapped \emph{massive} and \emph{gapless}
phases in bilayer graphene. The effective low energy theory in bilayer graphene
is constructed, and various discrete and continuous symmetries of the
non-interacting system is analyzed. Spinless fermions, placed in a quantizing
magnetic field is considered. The quantum anomalous Hall insulator is properly
defined. Constructing a particle-hole doubled 16 component Nambu-Dirac spinor,
we recognize all the possible fully gapped, and the gapless states, which, on
the other hand, split the parabolic dispersion into two anisotropic Dirac like
conical ones. A thorough symmetry analysis of all the ordered states is
performed. Altogether there are 8 insulating and 4 superconducting phases in
bilayer graphene, that can lead to fully gapped spectrum. Among the gapped
superconductors, \emph{three} are spin-singlet, which include uniform s-wave
and two spatially inhomogeneous, translational symmetry breaking Kekule
superconductors. The triplet pairing exhibits an f-wave symmetry. Besides the
gapped phases, there are 8 semimetallic and 8 gapless superconducting states in
total, available for fermions to condense into. We also find novel gapless
superconducting states, which break the translational symmetry, dubbed as
\emph{gapless-Fulde-Farrell-Larkin-Ovchinikov} superconductors. We also discuss
the role of Coulomb interaction, and propose various experimental tools to
determine the underlying ordered states.
