The invasion of the Greeks in ancient India refers primarily to the campaigns led by Alexander the Great, who invaded the northwestern regions of the Indian subcontinent in the 4th century BCE. Here are the key points regarding the Greek invasion of ancient India:

1. **Alexander’s Campaign**: In 326 BCE, Alexander the Great invaded the northwestern part of the Indian subcontinent after conquering Persia and parts of Central Asia. His campaign aimed to expand his empire and explore the regions of the Indian subcontinent.

2. **Battle of the Hydaspes**: One of the most significant battles during Alexander’s Indian campaign was the Battle of the Hydaspes (modern-day Jhelum River), fought in 326 BCE against King Porus of the Paurava kingdom. Despite being a formidable opponent, Porus was defeated by Alexander.

3. **Further Eastward Progress**: After defeating Porus, Alexander’s army wanted to press further east into the Indian heartland, but his troops were tired and mutinous. They refused to continue, and Alexander ultimately turned back, leaving his general, Seleucus Nicator, to govern the regions west of the Indus River.

4. **Greek Influence**: The Greek invasion had a lasting impact on Indian culture and history, particularly in the regions of Gandhara (modern-day Pakistan and Afghanistan). It led to cultural exchanges between Greek and Indian civilizations, resulting in Greco-Buddhist art and the incorporation of Greek artistic styles in Indian art.

5. **Legacy**: Although Alexander’s direct impact on Indian history was limited due to the brevity of his campaign and his army’s reluctance to go further east, his invasion highlighted the interconnectedness of ancient civilizations and contributed to the broader narrative of cultural exchange and diffusion in ancient times.

Overall, while the Greek invasion of ancient India under Alexander was relatively brief, it had significant implications for the cultural and historical developments in the northwestern regions of the subcontinent.