Brief descriptions do not work,. You need to learn it.

Complex Analysis. It is Calculus using Complex (imaginary) numbers.

A differencial equation, with several variables.(2) Partial Differential Equations and Applications

What Riemann made, it is use in General Relativitty. It is a more abstract approach to what a surface is and what the next thing you asked.(3) Differential Geometry

Calculus does not only need to be done in the standard xy-plane. Meaning on a sheet, it generalizes to Manifolds which are a much more general type of structure on which Calculus can do done.(4) Calculus on Manifolds

Also known as Calculus I.(5) Differential Calculus

The other course are extremely advanced and are only studied by people going into math in full detail.