  We develop a theory of the magnetic field-induced formation of Skyrmion
crystal state in chiral magnets in two spatial dimensions, motivated by the
recent discovery of the Skyrmionic phase of magnetization in thin film of
Fe$_{0.5}$Co$_{0.5}$Si and in the A-phase of MnSi. Ginzburg-Landau functional
of the chiral magnet re-written in the CP$^1$ representation is shown to be a
convenient framework for the analysis of the Skyrmion states. Phase diagram of
the model at zero temperature gives a sequence of ground states, helical spin
$\rightarrow$ Skyrme crystal $\rightarrow$ ferromagnet, as the external field
$B$ increases, in good accord with the thin-film experiment. In close analogy
with Abrikosov's derivation of the vortex lattice solution in type-II
superconductor, the CP$^1$ mean-field equation is solved and shown to reproduce
the Skyrmion crystal state.
