jacket : Sometimes used as another term for dust jacket, a protective and often decorative wrapper, usually made of paper which wraps around the binding of a book

reading copy : Indicates a book that is perfectly serviceable for reading. It may have a defect or damage.

As New : "the book is in the same immaculate condition in which it was published. There can be no defects, no missing pages, no library stamps, etc., and the dust jacket (if it was issued with one) must be perfect without any tears." Condition definition from AB Bookman's Weekly.