hi! here are a few previous threads to get you started

Spread of Buddhism

AMA: Daoism, Confucianism, Buddhism, the Three Great Traditions of China

How did Hinduism, Buddhism & Indian culture spread through SE Asia?

How did Buddhism spread to Japan and why it didn't spread to Europe?

When did Buddhism become the dominant religion in japan?

Why didn't Buddhism spread west to the Mediterranean like it spread east into China?

Why didn't Buddhism spread westward towards Europe despite the contact between the Greeks and the Indoiranians after the conquests of Alexander the Great?