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The ABC algorithm appeared in the 1990s in complex genetic problems where the likelihood of the model is impossible to compute or even reliably approximate. The principle behind ABC is that, for a generative model, simulated data associated with a value of the model parameter can be compared with the true data and assess whether or not this parameter is likely to have generated the data. ABC methods are now standard tools in many branches of statistics when likelihood computation is an issue, including dynamic models in signal processing and financial data analysis, networks and queuing models. While these methods suffer from calibration difficulties that make their implementation delicate, a wide range of ABC versions has emerged, inspired from sequential Monte Carlo techniques as well as econometric methods, Bayesian nonparametrics, and learning tools such as random forests. In addition, ABC claims to validity include convergence as an estimation method and consistency for model choice, which represents a large part of its uses in applied domains. The lecture will covers both these validation steps and different implementations of ABC algorithms and calibration of their parameters.