Introduction Part I 1. Definitions and immediate properties of the spaces $Ĥp(A)$ and $Ĥp(\partial A)$ 2. Jensen's inequality 3. Modulus automorphic functions 4. Blaschke factors and Blaschke products in $\hat {A}$ 5. Harmonic functions in $A$ 6. Modulus automorphic functions of bounded characteristic 7. The spaces $Ĥp_\alpha (A)$ 8. The Hilbert spaces $Ĥ2_\alpha (A)$ Part II 9. Preliminary remarks on the invariant subspace problem 10. The subspaces $Is[x]$ 11. The subspaces $Ds[x]$ 12. Completion of the characterization of doubly invariant subspaces 13. Szegö's theorem in an annulus
