Complex sentence: In July 1909 she began the habilitation process and by October of the same year her request had been approved and her post-doctoral studies began with a position as a private lecturer at the Department of Natural Sciences becoming the first female lecturer at ETH Zurich.
Split into simpler sentences: In July 1909 she began the habilitation process and by October of the same year her request was approved, she immediately began her post-doctoral studies. Eventually she managed to acquire a position as a private lecturer at the Department of Natural Sciences becoming the first female lecturer at ETH Zurich.