  Superconducting state in mesoscopic cylinder placed in the external magnetic
field is analyzed at general de Gennes boundary condition for the order
parameter. The lower and the surface critical fields of the cylinder are
calculated at different values of de Gennes "extrapolation length" $b$. For the
case of standard boundary condition (corresponding to $b\to \infty $) we use a
variational method to calculate the phase transitions between different
superconducting states. Based on the trial function for the order parameter, we
find an approximate solutions to the Ginzburg-Landau equations for the
Meissner, the single-vortex, and the giant-vortex states. The magnetization
curves of thin cylinders are calculated.
