Likelihood function is a very useful mathematical object in statistics. With it, you can perform the two main tasks in statistics,i.e. estimation and inference. If you can get the distribution right or the overall structural equation right, you can do all types of stats; univariate stats, multivariate stats , linear models, generalized linear model, mixture modeling, mixed effects model and even non parametric statistics to an extent. All of this can be done from scratch with one math object, “Likelihood function” + pen & paper + a plain vanilla optimization routine.