In the first part of this article, the author considers a nonlinear one dimensional stationary transport equation with general boundary condition, where the abstract boundary operator relates the outgoing flux to the incomming one. Recasting the problem as an operator equation of Hammerstein type, existence of solution is proved using Schauder’s fixed point theorem. Further, it is shown that the problem has at least one positive solution.In the last part of this paper, the results are generalized to the multidimensional case with vacuum boundary conditions. Under some restrictions like Lipschitz conditions on the collision frequency and scattering kernel, existence of a unique solution is also obtained using Banach contraction mapping theorem. Finally, the results are extended to multiplying boundary conditions.