Alexander, the great Macedonian emperor, is known to have conquered the world. Though his intention was to win Persia first. According to the ancient Greeks, his empire consisted of most parts of the world among which the Macedonian empire was the greatest of all. However, in reality, he did not conquer the WHOLE world, yes but he did WANT to.
He first wanted to win Persia because there was a clear animosity between Persia and Greece since Persians have enslaved several Greek zones in the past. Therefore, it was more of a revenge in his mind when he started.
Alexander was impressed with the different cultures he encountered while on his way to Greece. He was amazed to see and feel different cultures and hear several languages, numerous tales about the people of the East and their trade lines.
He had an army with lots of experience and technically advanced. This army was prepared to follow him anywhere and this was one of the reasons why he wanted to invade India.
Following the footsteps of his father Philip, Alexander just wanted to win Persia by trying to invade Greece twice and then winning the Greek colonies in addition to the seaside that's in West Turley currently.
Although his reason to invade India is still not known, it can be presumably due to the fact that he had an army with lots of experience and technologically sound that was prepared to accompany him anywhere in the world.
It can also be due to the fact that he had conquered Persia pretty easily and that too in a short time, so why not proliferate the remarkable Greek culture to other countries?