Where do I start read documentation about the FB API?

I want to integrate a PHP app with FB, but I don't know where to start reading the docs. In overview, I want users to join a closed FB group and link from there to a web page that will know the user's FB identity. The app will generate posts to the FB group and will tag all the other users of the app whose DNA matches. This app automates a cumbersome manual procedure that's in common use by armchair genealogists who often lack the computer skills to successfully locate and tag their matches.

I'm a very experienced (50+ years) programmer, and I'm not looking for someone to write my integration code for me. I just want a starting point in the voluminous documentation about the FB API.