  For bicovariant differential calculi on quantum groups various notions on
connections and metrics (bicovariant connections, invariant metrics, the
compatibility of a connection with a metric, Levi-Civita connections) are
introduced and studied. It is proved that for the bicovariant differential
calculi on $SL_{q}(N)$, $O_{q}(N)$ and $Sp_{q}(N)$ from the classification of
Schmuedgen, K. and Schueler, A. there exist unique Levi-Civita connections.
