  The structure of an isolated single vortex and the vortex lattice, and the
magnetization in a $d$-wave superconductor are investigated within a
phenomenological Ginzburg-Landau (GL) model including the mixture of the
$d_{x^2-y^2}$-wave and $d_{xy}$-wave symmetry. The isolated single vortex
structure in a week magnetic field is studied both numerically and
asymptotically. Near the upper critical field $H_{c2}$, the vortex lattice
structure and the magnetization are calculated analytically.
