In the seminar "Machine Learning in Earth System Science" we want to discuss the applicability of "Machine Learning" to different geoscientific data sets and modelling aproaches. The challenge in this application area is to integrate the statistics of the large geoscientific data sets into the existing atmospheric and Earth system models without violating the physical laws. First applications such as climate modelling, tracing of aerosols, CO2 flux prediction, nowcast weather prediction, and parameterization will be discussed in the context of this  seminar. Own work as well as current literature can be discussed.