linear algebra – multi-variant Gaussian

I have a few questions about the multivariate Gaussian formulation. I've seen a lot of videos and read Wikipedia, but I don't quite understand why things happen.


In this picture we have the general form of a multi-variate distribution.

My first question is roughly $ Sigma $ if it is the correlation or covariance matrix. I've seen different sources related to both, and I don't know why because they are different.

My second question concerns the form $ x ^ T Sigma x $ I do not understand this general form of wrapping a matrix in two x. WHY is that because we want x ^ 2? and if that's the case, why can't we do that? $ Sigma x ^ Tx $? Finally, that $ | Sigma | $ is the determination of $ Sigma $ but in the univariate case it is the standard deviation determined by $ Sigma $ equal to the standard deviation?

Any help on this intuition would help me a lot, thanks.