By, buy and bye are homophones in English; they are all pronounced /baɪ/ but have different spellings and their meanings and grammatical functions are completely different.
by

By is mainly used as a preposition. It has a wide range of meanings, as shown in the examples below.
We’ll be travelling by train.
My favourite painting is by Van Gogh.
I met him by chance yesterday.
He was amazed by their lack of professionalism.
buy

Buy is usually a verb. If you buy something, you obtain it by paying money for it.
He could not afford to buy a house.
Lizzie bought herself a mountain bike.
I’d like to buy him lunch.
Buy can also be used as a countable noun. If something is a good buy, it is of good quality and not very expensive.
This was still a good buy even at the higher price.
Bye

Bye and bye-bye are informal ways of saying goodbye.
We said bye at the door.
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