Is it permissible for me to keep two copies of a book that I received as a gift from the author, after I purchased 20 copies of the same book for the school library, or must I pay for them, or return them, or place them in the school library?

It is permissible to accept the two books as a gift from their author, because there is nothing to prevent their acceptance. This is because they are not given in exchange for an obligatory task, and the obligation has been fulfilled and the books were purchased before the gift. The gift does not influence the purchasing process in such a way as to suggest favoritism towards the author or seller.