A Timeline of Major Events in the Life of Alexander the Great

• 356 B.C. July - Alexander is born at Pella, Macedonia, to King Philip II and Olympias
• 336 - Alexander becomes ruler of Macedonia
• 334 - Wins Battle of the Granicus River against Darius III of Persia
• 333 - Wins Battle of Issus against Darius
• 332 - Wins siege of Tyre; attacks Gaza, which falls
• 331 - Founds Alexandria. Wins Battle of Gaugamela against Darius

"In the year 331 B.C. one of the greatest intellects whose influence the world has ever felt, saw, with his eagle glance, the unrivalled advantage of the spot which is now Alexandria; and conceived the mighty project of making it the point of union of two, or rather of three worlds. In a new city, named after himself, Europe, Asia, and Africa were to meet and to hold communion."
Charles Kingsley on the founding of the city of Alexandria

• 328 - Kills Black Cleitus for an insult at Samarkand
• 327 - Marries Roxane; Begins march to India
• 326 - Wins Battle of River Hydaspes against Porus; Bucephalus dies
• 324 - Troops mutiny at Opis
• 323 June 10 - Dies at Babylon in the palace of Nebuchadnezzar II

Sources: Arrian Campaigns of Alexander
BBC History

Also see Major Events in Ancient History Timeline for the broader context.