That manual is theirs, not yours. It's, with the apostrophe, is a contraction. Whose, without an apostrophe, is a possessive pronoun. My friend John, who is mother is a doctor, is studying medicine. My friend John, whose mother is a doctor, is studying medicine.
Handbooks have more information on apostrophes.
Some material was taken from a handout by Melinda Menzer. Ruth Vilmi. Feb.1995 .