Relativity Learn 4-D Geometry for General Relativity: Free Resources

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Self-studying general relativity can be challenging, particularly when it comes to understanding concepts like Christoffel symbols and geodesic equations. Many learners struggle to find introductory resources that provide clear definitions, explanations, and applications without delving into overly complex materials. Recommended free resources include lecture notes from Preposterous Universe and a set of lectures by Blau, which offer foundational insights into general relativity and 4-dimensional geometry. Additionally, video resources are suggested to complement the learning experience. These materials aim to provide complete proofs and practical applications to aid in understanding.
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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.
 
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