  The purpose of this paper is to introduce new invariants of Cohen-Macaulay
local rings. Our focus is the class of Cohen-Macaulay local rings that admit a
canonical ideal. Attached to each such ring R with a canonical ideal C, there
are integers--the type of R, the reduction number of C--that provide valuable
metrics to express the deviation of R from being a Gorenstein ring. We enlarge
this list with other integers--the roots of R and several canonical degrees.
The latter are multiplicity based functions of the Rees algebra of C.
