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ABO blood grouping divides human blood into four types based on the presence or absence of two specific antigens, antigen A and antigen B, on the red blood cell surface. These antigens are encoded by three alleles.

The allele immunoglobulin A, or simply allele A, codes for antigen A on the surface of the red blood cell. Similarly, allele B codes for antigen B.

The third allele - recorded as lowercase i and referred to as allele O - does not code for the antigen, meaning the red blood cells have neither antigen A nor antigen B.

Since the antigen's presence dictates the blood type, the alleles A and B are dominant over allele O, which does not produce any antigens. 

Humans are diploid organisms, and therefore they receive two copies of the alleles, one from each parent. A person with two copies of allele A or one copy of A and the recessive allele O has type A blood. Similarly, a person with two copies of allele B or one copy of B and the recessive allele O has type-B blood.

Having one copy of allele A and one of allele B results in type AB blood, an example of codominance, where both antigens are expressed on the red blood cell surface. Conversely, a person with both copies of the recessive non-antigen expressing allele will have type O blood.

Consider a male with blood type AB and a female with blood type O. Their progeny may inherit one copy of either allele A or B from the father and a recessive allele from the mother, resulting in offspring with type A or type B blood.

Rhesus factor is another blood typing system, this time based on the Rh antigen also called the D antigen on the red blood cells. The D antigen's presence is indicated with a plus sign, and its absence is marked with a minus sign.

Combining both typing systems, a person can be classified as A, B, AB, or O with positive or negative Rh factors.