Prerequisite: Linear algebra, multivariable calculus, probability theory, MATLAB programming. This course will introduce the principles of Inverse theory and data assimilation with applications to geophysics and other sciences. Both deterministic and stochastic viewpoints will be covered. Subjects studied will include topics such as least squares, generalized inverses, regularization, Kalman filter, adjoint method, etc. Techniques for solving nonlinear inverse and data assimilation problems will be also covered (200- level for Master students, 300-level for Ph.D. students with more home- and project work).