What is inverse theory in physics and geophysics? When do data-consistent models even exist? Topics may include the following: Multivariate regression modelling of discrete models, Bayesian approaches, maximum likelihood estimation, with errors and hypothesis testing, both classical and resampling(e.g. bootstrap). Continuous models where spatial resolution is a meaningful concept (Backus-Gilbert theory). The Singular Value Decomposition approach to modelling. Answerable and unanswerable questions in modelling. Singular Value Decompositions, norms such as L-1, L-infinity. Methods for non-linear modelling: e.g., Markov Chain Monte Carlo (MCMC), simulated annealing, genetic algorithms.