  The standard nonlinear perturbation theory of the gravitational instability
is extended to incorporate the nonlocal bias, redshift-space distortions, and
primordial non-Gaussianity. We show that local Eulerian bias is not generally
compatible to local Lagrangian bias in nonlinear regime. The Eulerian and
Lagrangian biases are nonlocally related order by order in the general
perturbation theory. The relation between Eulerian and Lagrangian kernels of
density perturbations with biasing are derived. The effects of primordial
non-Gaussianity and redshift-space distortions are also incorporated in our
general formalism, and diagrammatic methods are introduced. Vertex resummations
of higher-order perturbations in the presence of bias are considered.
Resummations of Lagrangian bias are shown to be essential to handle biasing
schemes in a general framework.
