Learn 4-D Geometry for General Relativity: Free Resources

[anachin6000]

I'm trying to self-study general relativity, but I encounter a problem. I can easily understand the ideas and the results, but there are some things related to 4-d geometry that I can't find, like what are Christoffel symbols and how to solve the equation of a geodesic line. I searched for those on the internet, but I found only complicated materials, not the introductory stuff, like definitions and explanations with applications.
So can anyone suggest some FREE introductory materials on general relativity and 4-d geometry?
I'm looking for something with complete proofs and applications.

 

[smodak]

Here you go

https://www.preposterousuniverse.com/grnotes/
http://www.blau.itp.unibe.ch/newlecturesGR.pdf

Also try these videos



Hope this helps.