You are talking about ABO blood group system, which is controlled by three independent genes. At present, the generally accepted "three alleles" theory holds that there are three alleles, A, B and O, which determine the inheritance of blood types A, B and O. The genotypes of type A blood are (aa, ao) type B (bb, bo) type O (oo) type AB.
Of course, there is more than one blood type system. According to erythrocyte surface antigen, it can be divided into 23 blood group systems, 5 blood group combinations and 2 blood group series.