  We review the physics of monolayer graphene in a strong magnetic field, with
emphasis on highly collective states that emerge from the weakly interacting
system because of correlations (emergent states). After reviewing the general
properties of graphene and of electrons in a magnetic field, we give a brief
introduction to the integer quantum Hall effect (IQHE) and the fractional
quantum Hall effect (FQHE) in a 2D electron gas as foundation to show that
monolayer graphene in a magnetic field exhibits both effects, but with
properties modified by the influence of the graphene crystal. After giving an
introduction to standard methods of dealing with emergent states for this
system, we show that an SO(8) fermion dynamical symmetry governs the emergent
degrees of freedom and that the algebraic and group properties of the dynamical
symmetry provide a new view of strongly correlated states observed in monolayer
graphene subject to a strong magnetic field.
