These are lecture notes by Apoorv Potnis of the lecture 'Aufgetakelte Hilberträume' or 'Rigged Hilbert Spaces', given by Prof. Frederic Schuller, as the eighth lecture in the course 'Theoretische Physik 2: Theoretische Quantenmechanik' in 2014 at the Friedrich-Alexander-Universität Erlangen-Nürnberg. While the original lecture is in German, these notes are in English and have been prepared using YouTube's automatic subtitle translation tool. The lecture is available at https://www.youtube.com/watch?v=FNJOyxOp3Ik&list=PLPO5pgr_frzTeqa_thbltYjyw8F9ehw7v&index=8 and at https://www.fau.tv/clip/id/4301.