  In this paper we give the first explicit enumeration of all maximal Condorcet
domains on $n\leq 7$ alternatives. This has been accomplished by developing a
new algorithm for constructing Condorcet domains, and an implementation of that
algorithm which has been run on a supercomputer.
  We follow this up by the first survey of the properties of all maximal
Condorcet domains up to degree 7, with respect to many properties studied in
the social sciences and mathematical literature. We resolve several open
questions posed by other authors, both by examples from our data and theorems.
We give a new set of results on the symmetry properties of Condorcet domains
which unify earlier works.
  Finally we discuss connections to other domain types such as non-dictatorial
domains and generalisations of single-peaked domains. All our data is made
freely available for other researches via a new website.
