Summary: The method of solution to the 2+1 dimensional Toda equation is described in some detail. This equation reduces directly to the well known Toda lattice in 1+1 dimension and, by an appropriate asymptotic reduction, to the Kadomtsev-Petviashvili equation in a continuous limit. The solution exhibits a number of interesting aspects depending on certain choices of signs, of which there are four, in the equation. For two choices of sign the equation is well-posed and linearly stable/unstable. For the other choices of sign the equation is linearly ill-posed. In these cases we can relate the solution to a boundary value problem and give a formal construction of the solution. For one choice of signs in the ill-posed case an analogue of the Sommerfeld radiation condition is developed in order to identify a unique solution. In general the method of solution of the “Toda molecule” equation requires an implementation of the d-bar technique to cases where the associated eigenfunctions possess both smooth regions of nonholomorphicity and a discontinuity across a curve, which in this problem is the unit circle. Special lump type solutions and solutions depending on suitable arbitrary functions are presented.