This volume contains a well-balanced choice of papers written by Ennio De Giorgi, an outstanding Italian mathematician of the 20th century. Many important papers were written by Ennio De Giorgi in Italian, hence the main motivation behind the project was to make them available to a larger public. In addition to their English translations, some of papers are also included in their Italian versions in order to give the reader a feeling of De Giorgi's original style (e.g. this is the case with the celebrated article, "Sulla differenziabilita e l'analiticita delle estremali degli integrali multipli regolari", one of the most important contributions to regularity theory). After a short biography, there is a description of the scientific work of Ennio De Giorgi, ending with contributions by Louis Nirenberg (remarks on some analytic works of Ennio De Giorgi) and Louis Caffarelli (De Giorgi's contribution to the regularity theory of elliptic equations). Then there is a collection of 43 papers (out of 152). In my opinion the volume, which covers all the main directions of the author's activities (measure theory, the 19th Hilbert problem, minimal hypersurfaces, G- and Γ-convergence, and foundations of mathematics) should be on the shelves of every mathematical library.

Reviewer:

oj