# Theory of Functions of Complex Variables

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In complex theory of functions one studies differentiable mappings into the complex numbers.

## Riemann surfaces

A Riemann surface is a one dimensional complex manifold. The easiest examples is the complex plane \(\mathbb{C}\).

## Conformal maps

A conformal mapping is an angle-preserving mapping.

## Real and imaginary parts of some functions

## Automorphic functions

An automorphic function is an analytic function, which is invariant under certain transformation. Elliptic functions are automorphic functions with double period.

## Surfaces and charts of the absolute value of some functions

## Elliptic functions

Elliptic functions are automorphic functions with double period.

## Others