Data assimilation seeks to optimally integrate different information sources to improve the state estimation of a complex system. It is also the prerequisite for effective ensemble forecasts. This chapter aims to provide an introduction to data assimilation. It starts with the mathematical derivation of the classical Kalman filter. The motivations behind the idea and different viewpoints on understanding the Kalman filter are also presented. Important concepts, such as observability and partial observations, are introduced in light of the multi-dimensional Kalman filter. Then, several nonlinear extensions of the Kalman filter are presented, including the extended Kalman filter, the ensemble Kalman filter, and the particle filter. The merits and applications of these methods are discussed. The continuous version of the Kalman filter, namely the Kalman-Bucy filter, and other data assimilation techniques, such as the smoother, and their applications are briefly studied at the end of this chapter.