My colleagues Alberto Carrassi, Olivier Talagrand and I, have organised a short course entitled Data assimilation in the geosciences - An Overview, during the EGU general assembly 2018. This has been a huge success, at least in terms of affluence: the room (65 seats) was full 15 minutes prior to the start of the course! You will find below the slides of the three courses.
Part I (Alberto Carrassi): Bayesian formulation of data assimilation. Gaussian approximations and the Kalman filter.
Part II (Olivier Talagrand): Variational methods. The ensemble Kalman filter.
Part III (Marc Bocquet): Localisation and inflation. The ensemble variational methods. Particle filters.
Here is a link to the review paper on which this short course is partially based on.