All Tennis Players How Many Grand Slams Has Albert Costa Won? Albert Costa i Casals (Eastern Catalan: [əlˈβɛɾ ˈkɔstə j kəˈzals]; born 25 June 1975) is a Spanish former professional tennis player.Albert Costa has won 1 Grand Slam.Albert Costa has won 1 Grand Slam. FacebookTwitterEmail How Many Grand Slams Has Madison Keys Won? How Many Grand Slams Has Jannik Sinner Won? How Many Majors Has John Isner Won?