  It is quite an interesting phenomenon in Topology that configuration spaces
on a manifold M are intrinsically related to certain mapping spaces from M. In
this paper we interpret and greatly expand on this relationship. Building
(mainly) on work of Segal, we introduce a new class of configuration spaces;
the particle spaces, and these include the classical configuration spaces of
distinct points, symmetric products, truncated products, divisor spaces,
positive and negative particles of McDuff, as well as many others. We show that
there are "scanning" maps that relate these spaces of particles on smooth
manifolds to section spaces of appropriate bundles. These correspondences we
prove are homology equivalences always and in some identifiable cases homotopy
equivalences. Applications of this to both algebraic geometry and algebraic
topology are given. We recover old as well as prove some new results on
configuration spaces, bounded multiplicity polynomials and loop spaces. Our
methods provide interesting insight into the stability phenomenon of
holomorphic mapping spaces discovered in the early eighties and asserting that
some spaces of rational maps give good topological approximations to second
loop spaces. Finally, we rediscover a beautiful space level description of the
classical duality theorems of Poincar\'e, Alexander and Lefshetz (first given
by Gajer), and further extend it to include Spanier-Whitehead duality.
