For men I can ask
"Is this his book?"
and
"Give him his book".
What is the parallel for the women?
"Is this her book"?
and
"Give her her book"?
If so, why do the men have two kinds of possessive forms (his, him) while the women have only one form (her, her)
Old English (for the sake of simplicity, English before the Norman Conquest in the year 1066) had declensions, like German. The feminine third person singular genitive and dative forms of the pronoun were the same (hire) whereas the masculine forms were his and him.
Umm. The part I'm having trouble with is your assertion that "him" is a possessive part. It's not. "Him" is a third-person singular pronoun used as an object.
Your tricky examples can be rephrased as
Give his book to him.
and
Give her book to her.
His and her are possessive determiners, and are followed by the referenced noun (book, in this case). Him and her are singular pronouns, and used as objects.
Your question might be better put as "Why is 'her' used both as a possessive determiner and as an object, while the masculine case uses 'his' and 'him'?"
Well, the best I can answer is "Just because". That's the way the language developed. Surely you don't think English is regular, do you?
See Wikipedia for a neat summary of pronouns.
"him" in the phrase was used because it serves as the object form for "his" And "her" as the object form of "she"... And as we can see both pronouns after a verb "give"( that means it deserves an object position). Leaving the clarified one apart, now there is something we call possessive adjective, example... His, her, their, its.... THEIR book, HIS ruler , HER chair... in this possessive adjective there is nothing like "him" or "she" qualifying any noun. So we can only say GIVE HER (object "her") HER BOOK(possessive adjective "her" qualifying the noun "book")... And GIVE HIM(object "him") HIS BOOK (possessive adjective "his" qualifying the noun "book")
