I am looking for literature or tutorial videos, which are concerned with the question of how multilevel markov chain monte carlo models are conducted in R or Mplus. Can someone help me?
However, brms is probably the easiest entry if you a new to MCMC and Bayes. There are a variety of different MCMC approaches and brms uses Hamiltonian (implemented in Stan). So if you want to know more about this form of MCMC you'd just need to look up Stan (though it isn't trivial if you have no physics background). Other MCMC approaches like Gibbs sampling (usually in jags or BUGS) or Metropolis-Hastings are easier to understand and in theory could be programmed directly in R (which some people do). However, usually one wants to run compiled code and using a specialised MCMC tool like Stan or jags makes sense. Packages like brms allow you to work in R and set up the model in Stan or jags for you.