Which kingdoms succeeded the empire of Alexander the great after his death?

The Empire split into four kingdoms, which would retain their sovereignty in order from least to longest: the Seleucids in Asia Minor and the Middle East, the Antigonids in Macedon (an area partly encompassing Greece), the Attalids in Pergamum (Asia Minor) and the Ptolemys in Egypt.

All four kingdoms were eventually incorporated into the Roman Republic.

After the Battle of Magnesia in 190 B.C., the final major battle in the Antiochan War, Antiochus is defeated by a conglomerate alliance of Rome, Pergamum, Rhodes and the Greek city state of Athens. Relying largely on its military authority and claim of monarchic divinity, the Seleucid Empire loses its power following the Treaty of Apamea in 188 B.C. which entails humiliating terms dictated by the Romans.

The kingdom of Macedon, after a series of four wars with Rome intermittedly spanning from 215 to 148 B.C., becomes increasingly weakened until Macedon loses its political sovereignty and becomes the Roman Province of Macedonia in 148 B.C.

The Kingdom of Pergamum in Asia Minor, founded by the Attalid dynasty, is peacefully left to Rome in 133 B.C. by Attalus III.

The Ptolemic dynasty in Egypt enjoys good relations with Rome until it is marred by the civil war between Caesar and Pompey, during which the advisors of the Ptolemic dynast execute Pompey, believing this will grant them favor with Caesar. Caesar, however, is infuriated at the execution of a worthy Roman citizen (a consul and military hero no less) at the hands of foreigners, and, trying to establish Cleopatra's faction on the throne, comes under serious assault by rioting crowds and hostile Egyptian forces in Alexandria until reinforcements arrive from across the Mediterranean. The independence of Egypt, with its massive agricultural potential for grain production, comes to an end when it becomes acquired by Gaius Julius Caesar Octavius (Octavian; Augustus following 27 B.C.) following his defeat of Marcus Antonius (Marc Antony) and Cleopatra's fleet at the naval Battle of Actium in 31 B.C. (off Greece's Eastern coast near the opening of the Ambracian gulf). Octavian then acquires hegemony over Egypt, marking an end to its political independence.