Where and who built the who built the worlds first library?

Ashurbanipal created the world's first libary in Assyria, this libary known as The Royal Library of Ashurbanipal, named after Ashurbanipal, the last great king of the Neo-Assyrian Empire, is a collection of thousands of clay tablets and fragments containing texts of all kinds (royal inscriptions, chronicles, mythological and religious texts, contracts, royal grants and decrees, royal letters, assorted administrative documents, and even what would be today called classified documents, reports from spies, ambassadors, etc.)
The collection written knowledge in some sort of repository is a practice as old as civilization itself. About 30,000 clay tablets found in ancient Mesopotamia date back more than 5,000 years. Archaelogists have uncovered papyrus scrolls from 1300-1200bc in the ancient Egyptian cities of Amarna and Thebes and thousands of clay tablets in the palace of King Sennacherib, Assyrian ruler from 704-681bc, at Nineveh, his capital city. More evidence turned up with the discovery of the personal collection of Sennacherib's grandson, King Ashurbanipal.
The Great Library of Alexandria, a public library open to those with the proper scholarly and literary qualifications, founded about 300bc. When Egypt's King Ptolemy I (305-282bc) asked, "How many scrolls do we have?", Aristotle's disciple Demetrius of Phalerum was on hand to answer with the latest count. After all, it was Demetrius who suggested setting up a universal library to hold copies of all the books in the world. Ptolemy and his successors wanted to understand the people under their rule and house Latin, Buddhist, Persian, Hebrew, and Egyptian works - translated into Greek.
So its on Ninevah by the Assyrians 
Hope it helps:)