As a political domain or domains , it was successively a province of the Umayyad Caliphate , the Caliphate of CÃ rdoba ( 929-1031 ) , and finally the Caliphate of CÃ rdoba 's taifa ( successor ) kingdoms . As a political domain or domains , it successively constituted a province of the Umayyad Caliphate , initiated by the Caliph Al-Walid I ( 711 â `` 750 ) ; the Emirate of CÃ rdoba ( c. 750 â `` 929 ) ; the Caliphate of CÃ rdoba ( 929 â `` 1031 ) ; and the Caliphate of CÃ rdoba 's taifa ( successor ) kingdoms .