Differentiable manifolds : forms, currents, harmonic forms / Georges de Rham

This is a very welcome translation of the french original [Variétés Différentiables (1955; Zbl 0065.324)]. The introduction of the original edition has been slightly modified. The new version contains the description of the content whereas the history of the problem and of the book itself is explained in a ”Préface á l’édition anglaise” by the author and in an ”Introduction to the English Edition” by S. S. Chern. In particular the author’s preface contains some autobiographical notes, and Chern’s introduction explains the link of the present book with work of W. V. D. Hodge, H. Weyl, H. Cartan, J.-P. Serre and others. The text of the book itself has not been changed except that the open question at the end of § 34 concerning harmonic forms on smooth but non-analytic manifolds has been answered and that there has been added a very last section § 35 on square summable harmonic forms.(Zentralblatt)