This book fills a gap: it comprehensively covers data assimilation and inverse methods by deriving them from a common theoretical basis in the description of which a modest level of mathematics is employed (assuming, however, familiarity with basic spatial statistics, Bayesian statistics and variational calculus). It continues with application of various popular data assimilation methods (weak/strong constraint variational methods, ensemble filters, smoothers) not only to illustrative textbook examples, but also to large scale examples such as the implementation of a Ensemble Kalman Filter in an ocean prediction system and an oil reservoir simulator. The structure and the style of the book reflect the authors experience in teaching this subject - it serves as a textbook for students as well as a reference book for researchers in the field as well as for those approching data assimilation from a field other than applied mathematics. The availability of code used in several of the data assimilation experiments make reading the book even more attractive. The book contains 16 chapters and an appendix, a large number of illustrating plots (often in color), and a very up-to-date list of references.