  In this paper we prove coincidence results concerning spaces of absolutely
summing multilinear mappings between Banach spaces. The nature of these results
arises from two distinct approaches: the coincidence of two \textit{a priori}
different classes of summing multilinear mappings and the summability of all
multilinear mappings defined on products of Banach spaces. Optimal
generalizations of known results are obtained. We also introduce and explore
new techniques in the field, for example a technique to extend coincidence
results for linear, bilinear and even trilinear mappings to general multilinear
ones.
