2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149556For 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.LaTeX2E, 20 pages; extended version, will appear in CMPQuantum Algebratext