  We study the fundamental groups of compact Sasakian manifolds, which we call
Sasaki groups. It is shown that all known K$\ddot{a}$hler groups are Sasaki, in
particular, all finite groups are Sasaki. On the other hand, we show there
exists many restrictions on the fundamental groups of compact Sasakian
manifolds. We also study the Abel-Jacobi map of a compact Sasakian manifold and
its applications to Sasaki groups.
