In 327 BC, after his conquest of Syria, Egypt and Persia Alexander made his way into India. Alexander and his army were driven by the desire to conquer the entire world. Through the writings of Herodotus the Greeks were also aware of the vast riches of India. The geopolitical scenario of north western India was also suitable for an easy conquest. There were a motley of independent monarchies and tribal republics which were fiercely independent and in perpetual conflict with each other. Among the rulers of these territories, two were well known Ambhi, the prince of Taxila, and Porus whose kingdom lay between the Jhelum and the Chenab. Together they might have effectively resisted the armies of Alexander. However, their own animosity prevented them from forming an alliance to challenge the Greeks and the Khyber pass remained unguarded.
After his conquest of Persia, Alexander moved on to Kabul, from where he marched to India through the Khyber pass and crossed the Indus. As Alexander crossed the Indus King Ambhi surrendered Taxila to Alexander without any resistance and offered allegiance.
However, Alexander's army was given stiff resistance in the Battle of Hydaspes (Jhelum River) by the armies of king Porus. Porus had an army of around 50,000 infantry, 4000 cavalry, 300 war chariots and 200 war elephants. This was the first time that the Macedonians saw war elephants and suffered severe losses. For one thing, the Macedonian horses would not go anywhere near the elephants. As result, they had to attack the giant beasts on foot. This resulted in the death of many of Alexander’s men who were either trampled under the elephants’ feet, impaled by elephants’ ivory tusks, or were killed by Indian archers sitting on top of the elephants. The battle raged for eight hours and the Macedonians suffered many casualties, more than in any other campaign. However, in the end the Macedonians overcame the forces of Porus. Alexander captured Porus, who had been wounded in the battle, and, like the other rulers he had defeated allowed him to continue governing his territory as his vassal. In this battle Alexanders horse, Bucephalus, was wounded and died. Alexander had ridden Bucephalus in everyone of his battles in Greece and Asia, so when it died, he was grief stricken. The victory was commemorated by the foundation of two towns, one named Nikaia, situated on the battlefield, and the other, named Boukephala, situated at the point whence Alexander had started to cross the Hydaspes.
After his victory over Porus, Alexander ventured further east conquering lands along the Indus river. However, his spies brought back news of the existence of the powerful Magdha Empire under the Nanda Dynasty eastwards in the Ganges planes. According to Plutarch, the Magdha army numbered 200,000 infantry, 80,000 cavalry, 8,000 chariots, and 6,000 war elephants, which was discouraging for Alexander's men and stayed their further progress into India."As for the Macedonians, however, their struggle with Porus blunted their courage and stayed their further advance into India. For having had all they could do to repulse an enemy who mustered only twenty thousand infantry and two thousand horse, they violently opposed Alexander when he insisted on crossing the river Ganges also, the width of which, as they learned, was thirty-two furlongs, its depth a hundred fathoms, while its banks on the further side were covered with multitudes of men-at‑arms and horsemen and elephants. For they were told that the kings of the Ganderites and Praesii were awaiting them with eighty thousand horsemen, two hundred thousand footmen, eight thousand chariots, and six thousand fighting elephants. And there was no boasting in these reports." - Plutarch, Parallel Lives, Life of Alexander. Facing mutiny Alexander turned back at the Beas river.This happened at the Hyphasis (modern Beas), the exact spot being believed to be at 'Kathgarh' in Indora tehsil of Himachal Pradesh.
Though Alexander's invasion was limited to the peripheries of the subcontinent and he never came in contact with any of the great states of India on the Ganges planes, it had its own socio-political effects. For one it paved the way for the political unification of the country and the rise of the first Indian empire under Chandragupta Maurya. Direct contact and trade was established between the Mediterranean civilizations and those of Punjab and western India. The establishment of Greek empire in the in the north-west of India gave rise to the Gandhara style of sculpture.