||A statistical theory for flexible macromolecules at interfaces has been developed. The theory is based on a lattice model in which the equilibrium set of molecular conformations in a concentration profile is evaluated, using a selfconsistent procedure. In this way, the Flory-Huggins theory for polymer solutions is extended to inhomogeneous solutions of macromolecules without any additional assumption. Apart from the Flory-Huggins polymer-solvent interaction parameter χ, a similar parameter χ s is used to describe the interaction of polymer segments with a solid interface. The average number of molecules in each particular conformation can be computed, so that a very detailed picture of the interfacial structure is obtained. Thus also the train, loop, and tail size distributions of adsorbed polymer can be calculated. In principle, there are no adjustable parameters in the theory. Moreover, there are no restrictions on the system parameters such as polymer concentration, chain length, number of species in a mixture or solvent quality, although in some cases numerical problems may occur. Results are given for adsorption of homopolymers, polydisperse polymer, polyelectrolytes, and star-branched polymer, for the structure of lipid bilayers and of the amorphous phase of semicrystalline polymer, and for the interaction between surfaces due to the presence of adsorbing or nonadsorbing polymer. Available experimental data on adsorption isotherms, bound fraction, layer thickness, surface fractionation, steric stabilization, and polymer bridging agree very well with the theoretical predictions.