This series of lectures is an introduction to the new, interdisciplinary and emerging discipline: data assimilation. DA is the solution of an inverse problem, where we seek an optimal estimation of the initial state of a dynamical system. It is the basis of all meteorological and climate predictions, but can be applied to any dynamic system, such as those found in ecology, population dynamics, disease propagation, etc. We will cover: (1) Definitions and notation, (2) Variational DA, (3) Statistical DA (Kalman filter, Ensemble filters, Bayesian and Nonlinear Filters), (4) Examples and applications.