  The melting of the Abrikosov vortex lattice in a 2D type-II superconductor at
high magnetic fields is studied analytically within the framework of the
phenomenological Ginzburg-Landau theory. It is shown that local phase
fluctuations in the superconducting order parameter, associated with low
energies sliding motions of Bragg chains along the principal crystallographic
axes of the vortex lattice, lead to a weak first order 'melting' transition at
a certain temperature $T_{m}$, well below the mean field $T_{c\text{}}$, where
the shear modulus drops abruptly to a nonzero value. The residual shear modulus
above $T_{m}$ decreases asymptotically to zero with increasing temperature.
Despite the large phase fluctuations, the average positions of Bragg chains at
fimite temperature correspond to a regular vortex lattice, slightly distorted
with respect to the triangular Abrikosov lattice. It is also shown that a
genuine long range phase coherence exists only at zero temperature; however,
below the melting point the vortex state is very close to the triangular
Abrikosov lattice. A study of the size dependence of the structure factor at
finite temperature indicates the existence of quasi-long range order with
$S(\overrightarrow{G}) \sim N^{\sigma}$, and $1/2<\sigma <1$, where
superconducting crystallites of correlated Bragg chains grow only along pinning
chains. This finding may suggest a very efficient way of generating pinning
defects in quasi 2D superconductors. Our results for the melting temperature
and for the entropy jump agree with the state of the art Monte Carlo
simulations.
