Primogeniture is the right, by law or custom, of the firstborn legitimate child to inherit the parent's entire or main estate in preference to shared inheritance among all or some children, any illegitimate child or any collateral relative. In most contexts, it means the inheritance of the firstborn son ; it can also mean by the firstborn daughter, or firstborn child.
Esau Sells His Birthright for Pottage of Lentils, a 1728 engraving by Gerard Hoet
Inheritance is the practice of receiving private property, titles, debts, entitlements, privileges, rights, and obligations upon the death of an individual. The rules of inheritance differ among societies and have changed over time. Officially bequeathing private property and/or debts can be performed by a testator via will, as attested by a notary or by other lawful means.
From William Hogarth's A Rake's Progress. "The Young Heir Takes Possession Of The Miser's Effects".