Consider a uniformly elliptic operator \(Lu \equiv Au+Vu\) defined on a bounded Lipschitz domain with principal part in divergence form and potential function \(V\) in an appropriate Kato class. The paper surveys basic theory for this operator that has been established by non-probabilistic methods. The paper is nicely organized and motivated. The Kato class, Dirichlet's problem and Green's function are introduced. Various results follow. They concern the local estimates for and continuity of the solutions of \(Lu=0\); estimates for the Green's function and \(L\)-harmonic measure; boundary behavior of positive solutions; and, in particular, a Fatou type theorem. A comparison of analytic and probabilistic approaches is given. A brief appendix views the operator with a drift term.