  In this paper, we study the rigidity and {\epsilon}-regularity theorems of
Ricci shrinkers. First we prove the rigidity of the asymptotic volume ratio and
local volume around a base point of a non-compact Ricci shrinker. Next we
obtain some {\epsilon}-regularity theorems of local entropy and curvature,
which improve the previous corresponding results essentially and use them to
study the structure of Ricci shrinkers at infinity. Especially, if the
curvature of a non-compact Ricci shrinker satisfies some natural integral
conditions, then it is asymptotic to a cone.
