During ICIAM 1995, in Hamburg, David Tranah approached Jacques-Louis Lions and myself and asked us if we were interested in publishing in book form our two-part article “Exact and approximate controllability for distributed parameter systems” which had appeared in Acta Numerica 1994 and 1995. The length of the article (almost 300 pages) was a justification, among several others, for such an initiative. While I was very enthusiastic about this project, J.L. Lions was more cautious, without being against it. Actually, his reservation concerning this book project was stemming from recent important developments on controllability related issues, justifying, in his opinion an in-depth revision of our article. Both of us being quite busy, the project was practically forgotten. As everyone knows in the Scientific Community, and elsewhere, Jacques-Lions passed away in June 2001, while still active scientifically. He largely contributed in making the Control of Distributed Parameter Systems a most important field where sophisticated mathematical and computational techniques meet with advanced applications. Therefore, when David Tranah renewed his 1995 suggestion during a conference of the European Mathematical Society held in Nice in February 2003, we thought that it would be a very nice way to pay to J.L. Lions the tribute he fully deserves. The idea was to respect as much as possible the original text, since it largely reflects J.L. Lions’ inspired scientific vision, and also its inimitable way at making simple complicated notions. On the other hand, it was also agreed that additional material should be included to make the text more up to date.