Because oC the large amount of material presented, we have been prevented from including all the topics originally announced for Part II of Linear Operators. The present volume includes all of the material of our earlier announcement associated with the classical spectral theorem for self adjoint operators in Hilbert space. While there are some isolated discussions of nousel fad joint operators, such as that giving the completeness of the generalized eigenfunctions of Hilbert-Schmidt operators in Section ХТ.в, the general theory of spectral operators and the discussion of nonselfadjoint differential boundary value problems have been postponed for inclusion in the forthcoming Part III of this treatise.