  Motivated by applications to a manifold of semilinear and quasilinear
stochastic partial differential equations (SPDEs) we establish the existence
and uniqueness of strong solutions to coercive and locally monotone SPDEs
driven by L\'{e}vy processes. We illustrate the main result of our paper by
showing how it can be applied to various types of SPDEs such as stochastic
reaction-diffusion equations, stochastic Burgers type equations, stochastic 2D
hydrodynamical systems and stochastic equations of non-Newtonian fluids, which
generalize many existing results in the literature.
