In this paper, we consider the problem of Adaptive model predictive control subject to exogenous disturbances. Using a novel set-based adaptive estimation, the problem of robust adaptive MPC is proposed and solved for a class of linearly parameterized uncertain nonlinear systems subject to state and input constraints. Two formulations of the adaptive MPC routine are proposed. A minmax approach is first considered. A Lipschitz-based formulation, amenable to real-time computations, is then proposed. A chemical reactor simulation example is presented that demonstrates the effectivenessof the technique.