Final answer:
Alexander the Great inherited his father's plan to invade the Persian Empire, overcoming the slow Persian military assembly with his well-trained 45,000-strong Macedonian army, achieving victories at Issus and Gaugamela. His adroit blend of military tactics and political strategies such as cultural integration ensured the retention of power in conquered Persian territories.
Step-by-step explanation:
Alexander the Great inherited his father Philip II's grand project of invading and conquering the Persian Empire promptly after quelling internal threats. Upon becoming king, Alexander swiftly demonstrated his military prowess, dealing with Thracian invasions and Theban rebellion before turning the attention of the Macedonian army towards Persia. His small yet superior fighting force of approximately 45,000 men faced a potential Persian army of nearly 300,000. However, the Persian military strategy was sluggish, and their assembly of vast armies was too slow, allowing Alexander's highly-trained and agile forces to conquer Persian lands piece by piece.
At the decisive battles of Issus and Gaugamela, the Macedonian army's discipline, superior tactics, and the personal leadership of Alexander trumped the larger but less coordinated Persian forces. Alexander's strategic genius in absorbing Persian culture and offering alliances to conquered territories also helped maintain and spread his power over these regions. Post-conquest, the former Persian Empire largely remained under Greek and Macedonian rule, partially due to Alexander's political savviness in integrating Persian structures and customs into his administration.