Advanced versions of the inverse function theorem

"This short opus is dedicated to the bright memory of the distinguished mathematician Gabriela Kohr and her mathematical heritage. Gabriela Kohr's contribution to analysis of one and several complex variables brought new knowledge into the modern theory as well as new colors to the subject. During our meetings with Gabriela at various conferences she always proposed some interesting and often nonstandard questions related to classical issues as well as new directions. It is worth to be mentioned her excellent book [50] together with Ian Graham on classical and modern problems in Geometric Function Theory in complex spaces (see also, [46], [56], [27], [22], [24], [49] and [48])."