In the Books table try placing the AuthorID PrimaryKey in that table. Oooops, back this baby up a sec. You are using Author_Name as the primary key? What if you happen to have two authors with the same names? Set up a unique identifier, either an AutoNumber as AuthorID or create one of your own that makes each Author unique and be sure to set it to Indexed / No Duplicates. Your relationships are set up as One-To-Many correct?? One question, why are you needing a CommandButton to add the Author into the table?
Wow, these late hours are getting to me. I missed something else too. You have Author_Name as the PrimaryKey field. You have Author_FirstName and Author_LastName. So WHAT exactly goes in the Author_Name key field???