A new universal conserved current, depending on a field and two variations of the field, is defined and
shown to provide a general approach to the covariant description of the phase space of a Lagrangian field
theory. The global symplectic — and in certain cases Kahlerian — geometry of phase space is examined for
particular models. The moduli space of Riemann surfaces makes an unexpected appearance in three dimensional field theory; in particular, gravity. A brief discussion of quantization concludes a mainly classical treatment of field theory and action principles.