Preface and historical note.- Laplace-Beltrami operator.- Harmonic functions.- Quasiharmonic functions.- Bounded biharmonic functions.- Dirichlet finite biharmonic functions.- Bounded dirichlet finite biharmonic functions.- Harmonic, quasiharmonic, and biharmonic degeneracies.- Riesz representation of biharmonic functions.- Biharmonic Green's function ?.- Biharmonic Green's function ?: Definition and existence.- Relation of O ? N to other null classes.- Hadamard's conjecture on the Green's function of a clamped plate.