Data assimilation involves combining observations with model output to obtain a consistent, evolving three-dimensional picture of the atmosphere. This process is used to generate an initial state for producing forecasts at operational weather forecast centres. Data assimilation can also provide added value to observations by filling in data gaps and inferring information about unobserved variables. In this course, common methods of data assimilation (optimal interpolation, Kalman filtering, variational methods) are introduced and derived in the context of estimation theory. A hands-on approach will be taken so that methods introduced in the lectures will be implemented in computer assignments using toy models.