Continuation of the course "Introduction of Computersimulation I" of WS20/21. The focus of this part II will be on advanced methods for Monte Carlo computer simulations such as cluster update algorithms (Wolff single and Swendsen-Wang multiple cluster variants), multigrid update algorithms, and generalized ensemble methods (simulated tempering, parallel tempering, multicanonical, Wang-Landau). Their performances will be assessed by analyzing the statistical errors respectively autocorrelation times. Also refined reweighting procedures will be introduced and demonstrated how these tools can be put to good use in scaling and finite-size scaling analyses in the vicinity of phase transitions (critical region around second-order transitions and phase coexistence at first-order transitions) and for complex systems with rugged free-energy landscapes such as spin glasses and proteins. The methods will be illustrated with applications to selected spin and polymer systems.