  Ginzburg-Landau theory is used to study the properties of single vortices and
of the Abrikosov vortex lattice in a $d_{x^2-y^2}$ superconductor. For a single
vortex, the $s$-wave order parameter has the expected four-lobe structure in a
ring around the core and falls off like $1/r^2$ at large distances. The
topological structure of the $s$-wave order parameter consists of one
counter-rotating unit vortex, centered at the core, surrounded by four
symmetrically placed positive unit vortices. The Abrikosov lattice is shown to
have a triangular structure close to $T_c$ and an oblique structure at lower
temperatures. Comparison is made to recent neutron scattering data.
