We establish the equivalence of three versions of a finite dimensional
quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak
$C^*$-Hopf algebra introduced by G. Bohm, F. Nill and K. Szlachanyi (with an
involutive antipode), and a Kac bimodule -- an algebraic version of a Hopf
bimodule, the notion introduced by J.-M. Vallin. We also study the structure
and construct examples of finite dimensional quantum groupoids.
