Approximate Bayesian Computation (ABC) methods is a technique usedto make parameter inference and model selection of issues of intractablelikelihood and complex models.In this thesis, we briefly discuss the philosophy of Bayesian inference andelaborated more on the definition, implementation and demonstration ofthe three ABC algorithms. We wanted to know the efficiency of the ABCmethods in computing the samples of posterior parameters compare to theanalytically computation of the posterior parameters. The ABC algorithmis applied on two simple toy examples. In these toy examples, the posteriorpdf is known before implementing the algorithm. We further compare thesamples of posterior parameter values obtained using ABC to the true pos-terior and hence verify the accuracy of the algorithm.