Patrilineality (a.k.a agnatic kinship) is a system in which one belongs to one's father's lineage; it generally involves the inheritance of property, names or titles through the male line as well.
A patriline is a line of descent from a male ancestor to a descendant (of either sex) in which the individuals in all intervening generations are male. In a patrilineal descent system (= agnatic descent), an individual is considered to belong to the same descent group as his or her father. This is in contrast to the less common pattern of matrilineal descent.
The agnatic ancestry of an individual is that person's pure male ancestry. An agnate is one's (male) relative in an unbroken male line: a kinsman with whom one has a common ancestor by descent in unbroken male line.
The fact that the Y chromosome is paternally inherited enables patrilines, and agnatic kinships, of individuals to be traced through genetic analysis.