This course is intended to present fundamental material to understand and practice inversion of geophysical data. The emphasis is on a formal presentation of the relevant background theory. A first tier of the class will be focused on the statistical approach to inversion of experimental data, incorporating a priori information, constraints from measurements and theoretical insight. The rest of the class will focus on the optimization problem in a Hilbert space, including the definition of cost functions and regularization techniques. The theory will be discussed in the context of typical problems of geophysical relevance including gravity, faulting, seismology and signal processing. Students are assumed familiar with linear algebra, calculus and statistics.