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1 Battle of Gugemela: The Battle of Gaugamela (/mil/; Greek: ), also called the Battle of Arbela (Greek: ), was the decisive battle of Alexander the Great's invasion of the Persian Achaemenid Empire. In 331 BC Alexander's army of the Hellenic League met the Persian army of Darius III near Gaugamela, close to the modern city of Dohuk(Iraqi Kurdistan). Though heavily outnumbered, Alexander emerged victorious due to his army's superior tactics and his deft employment of light infantry. It was a decisive victory for the Hellenic League and led to the fall of the Achaemenid Empire.
2 Battle of Issus: The Battle of Issus occurred in southern Anatolia, on November 5, 333 BC between the Hellenic League led by Alexander the Greatand the Achaemenid Empire, led by Darius III, in the second great battle of Alexander's conquest of Asia. The invading Macedonian troops defeated Persia. After the Hellenic League soundly defeated the Persian satrapsof Asia Minor (led by Greek mercenary Memnon of Rhodes) at the Battle of the Granicus, Darius took personal command of his army. He gathered reinforcements and led his men in a surprise march behind the Hellenic advance to cut their line of supply. This forced Alexander to countermarch, setting the stage for the battle near the mouth of the Pinarus River and the town of Issus.
3 Battle of Hydespass or Jehlum: The Battle of the Hydaspes was fought in 326 BC between Alexander the Great and King Porus of the Paurava kingdom on the banks of the river Jhelum (known to the Greeks as Hydaspes) in the Punjab region of the Indian subcontinent (modern-day Punjab, Pakistan). The battle resulted in a complete Greekvictory[a] and the annexation of the Punjab, which lay beyond the far easternmost confines of the already absorbed Persian Empire, into the Macedonian Empire.
There is battle of Tyre also ...Tyre was considered invincible but Alexander conquered it ..catapults were used for first time ever in it.
Though the popular and historical aspect says that Alexander won Battle of hydespases...there are few conspiracy theorists who says it was a tie or even Porus won( though no historical book of world say so. This theory gained ground when Oliver Stone Alexander showed no result. Though the film was absolutely rubbished by Historians and was a huge flop) ...it is fact that Porus was killed by his Macedonian general ..and it is also fact that there are coins relating to Alexander's win still available ...Also Chandra Gupta later forced Greeks out of paurav territory...Moreover Indian folklores also say Porus fought valiantly but lost...Roman texts, enemies of Greece says Alexander won ... And then there are other records which are not greek which say Alexander won but suffered heavily but was willing to go further...