The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.

In the period since the original four volumes of Phillip Griffiths's Selecta were published (Selected Works of Phillip A. Griffiths with Commentary), Parts 1-4, Collected Works, Volume 18), Griffiths has continued to produce beautiful and important work. The current two-part publication brings Griffiths's Selecta up to date by including the majority of his recent articles, as well as two older papers on differential geometry whose length had precluded their inclusion in the original Selecta. The papers are organized along the three main topics: Differential Geometry and Hodge Theory (Part 5) and Algebraic Cycles (Part 6). In addition to his papers, Griffiths has been an author of a number of research monographs. To give the reader an overview of what these monographs contain, introductions to some of these are also included.