Takshashila Uniersity in India is one of the main contenders for the prized title of the "first university." It was well known as an institution of higher learning in ancient India.
Other contenders are
1. Nalanda University in India
2. Al-Azhar University in Cairo, Egypt, founded at the same time as the City of Cairo, in (approximately) 969 AD.
3. Qarawiyyin Mosque in Fez, Morroco.
4. The Academy of Plato, founded in 4th Century Greece.