  We complete the kinetic theory of two-dimensional (2D) point vortices
initiated in previous works. We use a simpler and more physical formalism. We
consider a system of 2D point vortices submitted to a small external stochastic
perturbation and determine the response of the system to the perturbation. We
derive the diffusion coefficient and the drift by polarization of a test
vortex. We introduce a general Fokker-Planck equation involving a diffusion
term and a drift term. When the drift by polarization can be neglected, we
obtain a secular dressed diffusion (SDD) equation sourced by the external
noise. When the external perturbation is created by a discrete collection of
$N$ point vortices, we obtain a Lenard-Balescu-like kinetic equation reducing
to a Landau-like kinetic equation when collective effects are neglected. We
consider a multi-species system of point vortices. We discuss the process of
kinetic blocking in the single and multi-species cases. When the field vortices
are at statistical equilibrium (thermal bath), we establish the proper
expression of the fluctuation-dissipation theorem for 2D point vortices
relating the power spectrum of the fluctuations to the response function of the
system. In that case, the drift coefficient and the diffusion coefficient
satisfy an Einstein-like relation and the Fokker Planck equation reduces to a
Smoluchowski-like equation. We mention the analogy between 2D point vortices
and stellar systems. In particular, the drift of a point vortex in 2D
hydrodynamics is the counterpart of the Chandrasekhar dynamical friction in
astrophysics. We also consider a gas of 2D Brownian point vortices described by
$N$ coupled stochastic Langevin equations and determine its mean and mesoscopic
evolution. In the present paper, we treat the case of unidirectional flows but
our results can be straightforwardly generalized to axisymmetric flows.
