  We report the application of the nonlinear $\sigma$ model to study the
multi-skyrmion problem in the quantum Hall ferromagnet system. We show that the
ground state of the system can be described by a ferromagnet triangular Skyrme
lattice near $\nu=1$ where skyrmions are extremely dilute. We find a transition
into antiferromagnet square lattice by increasing the skyrmion density and
therefore $|\nu-1|$. We investigate the possibility that the square Skyrme
lattice deforms to a single skyrmion with the same topological charge when the
Zeeman energy is extremely smaller than the Coulomb energy. We explicitly show
that the energy of a skyrmion with charge two is less than the energy of two
skyrmions each with charge one when $g \leq g_c$. By taking the quantum
fluctuations into account, we also argue the possibility of the existence of a
non-zero temperature Kosterlitz-Thouless and a superconductor-insulator phase
transition.
