The key word, giving the motivation of the most contributions in this volume, is BRIDGES. The title of the volume is just the slogan under which the Conference was announced at the beginning of the year 1998. This slogan requires some explanations. The noun "bridge" and the verb "to bridge" became, in the last decades, one of the most frequent metaphors to which a reference is made when the adopted approach crosses different fields. Is it equivalent to what is traditionally called interdisciplinarity? It seems that "bridge" is in some sense less and in some other sense more. We will not speak of bridging mathematics and mechanics, because their .collaboration is very old. "Bridge" is reserved for fields or trends not yet connected or insufficiently connected.