  We develop an existence, regularity and potential theory for nonlinear
integrodifferential equations involving measure data. The nonlocal elliptic
operators considered are possibly degenerate and cover the case of the
fractional $p$-Laplacean operator with measurable coefficients. We introduce a
natural function class where we solve the Dirichlet problem, and prove basic
and optimal nonlinear Wolff potential estimates for solutions. These are the
exact analogs of the results valid in the case of local quasilinear degenerate
equations established by Boccardo & Gallou\"et \cite{BG1, BG2} and
Kilpel\"ainen & Mal\'y \cite{KM1, KM2}. As a consequence, we establish a number
of results which can be considered as basic building blocks for a nonlocal,
nonlinear potential theory: fine properties of solutions, Calder\'on-Zygmund
estimates, continuity and boundedness criteria are established via Wolff
potentials. %In particular, optimal Lorentz spaces continuity criteria follow.
A main tool is the introduction of a global excess functional that allows to
prove a nonlocal analog of the classical theory due to Campanato \cite{camp}.
Our results cover the case of linear nonlocal equations with measurable
coefficients, and the one of the fractional Laplacean, and are new already in
such cases.
