Abstract: The Kicked Rotator is one of the central models in studies of chaos theory. Its quantization was the subject of great interest in the 1980s, but since the 1990s, interest faded. I hope to rekindle interest in this subject. This second working seminar will consist in three parts. In the first I will start by recapitulating the classical Kicked Rotator and its quantization. I will then proceed to recall its connection to Schrodinger operators. In the second part I will start by talking about basic examples of the problem of small divisors in quantum mechanics and following that, I will present perturbation theory for the quantum Kicked Rotator and my results on this field. In the final part I will review what remains to be done and, hopefully, a lively discussion will ensue. The small divisors problem in the quantum Kicked Rotator (II)