I. Elementary Theory -- I. Locally compact fields -- II. Lattices and duality over local fields -- III. Places of A-fields -- IV. Adeles -- V. Algebraic number-fields -- VI. The theorem of Riemann-Roch -- VII. Zeta-functions of A-fields -- VIII. Traces and norms -- II. Classfield Theory -- IX. Simple algebras -- X. Simple algebras over local fields -- XI. Simple algebras over A-fields -- XII. Local classfield theory -- XIII. Global classfield theory -- Index of definitions