@MoreAnonymous John Baez lists some recommended GR books on the intro page of his GR tutorial
math.ucr.edu/home/baez/gr/gr.html The tutorial itself is quite good, although as he says, it's a bit disorganised, and it's a bit old so it just uses HTML for equations, not MathJax. But it's aimed at mathematicians who are comfortable with linear algebra who want to understand the mathematics of GR.