Adsorption at fluid-solid interfaces is considered in the framework of a lattice with boundaries. Using ideas proposed by S. Ono and S. Kondo (in "Molecular Theory of Surface Tension in Liquids" (S. Flugge, Ed.), Encyclopedia of Physics, Vol. IO, p. 134. Springer-Verlag, Berlin, 1960), a lattice model is derived, both rigorously and phenomenologically, and applied to macro-, meso-, and microporous adsorbents by imposing different boundary conditions. It is shown that this lattice theory can predict the entire spectrum of behavior observed when gases, liquids, or supercritical fluids adsorb on solid surfaces. In particular, it is able to predict steps in the isotherms, scaling behavior near saturation conditions, supercritical behavior, and adsorption hysteresis. It is shown that there is a profound analogy in the adsorption behavior of a one-component gas to that of a binary liquid mixture. This analysis leads to a new classification of physisorption isotherms for fluid/solid equilibria.