Hi! Sorry for the delay, but here I bring you some recommendations for the New Year.
My favourite book is A Short Course in GR by Foster and Nightingale. It's brief and well structured. First chapter explains the required Math. The second one is the fundations of GR. The following ones apply GR to different systems. And the final one is about Cosmology. It can be followed on your own as far as you already know multivariable Calculus.
If you want to go deeper into the Maths I recommend you The Geommetry of Physics by Frakel. This is a huge book I only recommend as reference. Otherwise it can turn into a rabbit hole. Fascinating but goes into much more detail than required.
And the standard textbook I've used on my lectures is the Weinberg Cosmology textbook. Content is exhaustive, examples and exercises abundant, explanations go from fine to great. But I really don't like the structure of the book, it goes back and forth a lot and the Maths are explained on chapters on the go as they are required to the extent where topics that are a natural extension of one another (such as covariant derivatives and parallel transport) may be separated by several chapters.
Finally, if you feel confident and have an easy time with Foster's and Weinberg's books, go take a look at Landau vol. 2 on Classical Fields. I find the notation and the explanaitions are dense as hell, but overall worth it. Also, most of the book deals with general fields or the Electromagnetic one, but there are some chapters on the gravitational field following GR (it's also worth mentioning that there's little to no focus on the Cosmology of the Universe, just the GR formalism).
I hope you find these recommendations helpful. As a TL;DR I'd say: follow Foster's on your own, Weinberg for lectures.