What type of mathematica is this on the picture. When I start to study relativity, it appears and I don't understand it. 

Try math Forum.

What type of mathematics must I do to understand this mathematics in the picture below?

It is tensor calculus, and differential geometry.

Perhaps it would be better to start with Special Relativity first, which is simpler, and work your way up from there.

21 hours ago, Lizwi said:

What type of mathematica is this on the picture. When I start to study relativity, it appears and I don't understand it. 

Look here

https://www.grc.nasa.gov/www/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf

Tensor analysis.

 

A very complete classic book of which affordable paperback editions exist:

https://www.amazon.es/Tensors-Differential-Variational-Principles-Mathematics/dp/0486658406

1 hour ago, Markus Hanke said:

It is tensor calculus, and differential geometry.

Perhaps it would be better to start with Special Relativity first, which is simpler, and work your way up from there.

Ignore my answer on thread "Four-vector" and follow this excellent tip by Markus. Studiot's recommendation looks fine. It's just that I'm not familiar with it.

The simpler toys to play with are called "affine tensors". They do not depend on the point of space you're considering. Special Relativity is the place to start --> nothing depends on the location. Then make tensors depend on the point of space --> tensor analysis. You will become familiar with a monster called "the connection", and "the Riemann tensor" and everything else come from that "connection".

!

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