This introduction to Bayesian statistics presents themain concepts as well as the principal reasons advocatedin favour of a Bayesian modelling. We coverthe various approaches to prior determination as wellas the basis asymptotic arguments in favour of usingBayes estimators. The testing aspects of Bayesianinference are also examined in details. Bayesian inference, Bayes model choice,foundations, testing, non-informative prior, Bayesiannonparametrics, Bayes factor