  Based on a two dimensional odd-parity superconducting order parameter for
Sr_2RuO_4 with p-wave symmetry, we investigate the single vortex and vortex
lattice structure of the mixed phase near H_{c1}. Ginzburg-Landau calculations
for a single vortex show a fourfold structure with an orientation depending on
the microscopic Fermi surface properties. The corresponding extended London
theory is developed to determine the vortex lattice structure and we find near
H_{c1} a centered rectangular vortex lattice. As the field is increased from
H_{c1} this lattice continuously deforms until a square vortex lattice is
achieved. In the centered rectangular phase the field distribution, as
measurable through \mu-SR experiments, exhibits a characteristic two peak
structure (similar to that predicted in high temperature and borocarbide
superconductors).
