The NATO Advanced Study Institute on Numerical Taxonomy took place on the 4th - 16th of July, 1982, at the Kur- und Kongresshotel Residenz in Bad Windsheim, Federal Republic of Germany. This volume is the proceedings of that meeting, and contains papers by over two-thirds of the participants in the Institute. Numerical taxonomy has been attracting increased attention from systematists and evolutionary biologists. It is an area which has been marked by debate and conflict, sometimes bitter. Happily, this meeting took place in an atmosphere of "GemUtlichkeit", though scarcely of unanimity. I believe that these papers will show that there is an increased understanding by each taxonomic school of each others' positions. This augurs a period in which the debates become more concrete and specific. Let us hope that they take place in a scientific atmosphere which has occasionally been lacking in the past. Since the order of presentation of papers in the meeting was affected by time constraints, I have taken the liberty of rearranging them into a more coherent subject ordering. The first group of papers, taken from the opening and closing days of the meeting, debate philosophies of classification. The next two sections have papers on congruence, clustering and ordination. A notable concern of these participants is the comparison and testing of classifications. This has been missing from many previous discussions of numerical classification.