Most of these are books I use one way or another for rapport or to get to know her better. I don't use all of these on every woman but sometimes when you are screening each other for serious relationship (or super long term like marriage and kids), they are useful.

Instant Rapport (for learning styles and a test)

5 Love Languages by Gary Chapman (very useful for a relationship so that she is receiving affection in a way that works for her. As an example, sometimes gifts are a lot less important to an individual woman than say....acts of service.

Fabulous book of questions (this can be earlier on, take turns asking each other a question from it)

365 questions for couples (a little later on: take turns asking each other a question from it)

Kokology 1 and 2 (Japanese personality games, can be early on)

Definitive book of body language (ok, there are 3 books i like better, but those are dating books so don't meet this post's theme)

Unmasking the Face (if you need help reading emotions)

Myers-Briggs books (and test) can be helpful as well conceptually, even if not particularly reliable. Certainly knowing if she is an E or I is useful.