Inverse Modeling of the Ocean and Atmosphere is a graduate-level textbook for students of oceanography and meteorology, and anyone interested in combining computer models and observations of the hydrosphere or solid earth. A step-by-step development of maximally-efficient inversion algorithms, using ideal models, is complemented by computer codes and comprehensive details for realistic models. Variational tools and statistical concepts are concisely introduced, applications to contemporary research models are examined in detail and further advanced research topics are discussed.