  If X is a discrete abelian group and B a finite set, then a cellular
automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts.
If g is a real-valued function on B, then, for any b in B^X, we define G(b) to
be the sum over all x in X of g(b_x) (if finite). We say g is `conserved' by F
if G is constant under the action of F. We characterize such `conservation
laws' in several ways, deriving both theoretical consequences and practical
tests, and provide a method for constructing all one-dimensional CA exhibiting
a given conservation law.
