Abstract
We present a theory for a vortex lattice in a layered superconductor, with very weak coupling between the layers. We use the Lawrence-Doniach model to show that only the component of the magnetic field that is perpendicular to the layers can give rise to an Abrikosov vortex lattice. The parallel component penetrates completely into the superconductor, which behaves as if it were magnetically transparent. The actions of these two components are very different, and almost completely decoupled. We find the lower critical fields, as well as the torque.