  This is the first in a series of papers math.AG/0503029, math.AG/0410267,
math.AG/0410268 on "configurations" in an abelian category A. Given a finite
partially ordered set (I,<), an (I,<)-configuration (\sigma,\iota,\pi) is a
finite collection of objects \sigma(J) and morphisms \iota(J,K) or \pi(J,K) :
\sigma(J) --> \sigma(K) satisfying some axioms, where J,K are subsets of I.
Configurations describe how an object X in A decomposes into subobjects, and
are especially useful for studying stability conditions on A.
  This paper defines and motivates the idea of configurations, and explains
some natural operations upon them -- subconfigurations, quotient
configurations, refinements, improvements and substitution. Then we study
moduli spaces of (I,<)-configurations in A, using the theory of Artin stacks.
We prove well-behaved moduli stacks exist when A is an abelian category of
coherent sheaves or vector bundles on a projective K-scheme P, or of
representations of a quiver Q. We define many natural 1-morphisms between the
moduli stacks, some of which are representable or of finite type.
  The sequels will apply these results to construct and study
infinite-dimensional algebras associated to a quiver Q, and to define systems
of invariants of a projective K-scheme P that "count" (semi)stable coherent
sheaves and satisfy interesting identities.
