A Library is an institution that holds books and other form of stored information for use by the public. It is usual for it to be housed in rooms of a building where items of the collection are lent to members with or without payment while providing various other services for it's community of users.
"I need to go and read in the Library this evening."
Libary is a common misspelling of the actual word, library. This is considered redundant as a word and is often termed as incorrect.