This volume is a result of a meeting which took place in June 1986
at 'll Ciocco" in Italy entitled 'Deformation theory of algebras
and structures and applications'. It appears somewhat later than is
perhaps desirable for a volume resulting from a summer school. In
return it contains a good many results which were not yet available
at the time of the meeting. In particular it is now abundantly
clear that the Deformation theory of algebras is indeed central to
the whole philosophy of deformations/perturbations/stability. This
is one of the main results of the 254 page paper below (practically
a book in itself) by Gerstenhaber and Shack entitled "Algebraic
cohomology and defor mation theory". Two of the main
philosphical-methodological pillars on which deformation theory
rests are the fol lowing * (Pure) To study a highly complicated
object, it is fruitful to study the ways in which it can arise as a
limit of a family of simpler objects: "the unraveling of
complicated structures" . * (Applied) If a mathematical model is to
be applied to the real world there will usually be such things as
coefficients which are imperfectly known. Thus it is important to
know how the behaviour of a model changes as it is perturbed
(deformed).
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