  This paper, written in 1998, aims to clarify various higher categorical
structures, mostly through the theory of generalized operads and
multicategories. Chapters I and II, which cover this theory and its application
to give a definition of weak n-category, are largely superseded by my thesis
(math.CT/0011106), but Chapters III and IV have not appeared elsewhere. The
main result of Chapter III is that small Gray-categories can be characterized
as the sub-tricategories of the tricategory of 2-categories, homomorphisms,
strong transformations and modifications; there is also a conjecture on
coherence in higher dimensions. Chapter IV defines opetopes and a category of
n-pasting diagrams for each n, which in the case n=2 is a definition of the
category of trees.
