In Chap. 2, we present the summary of coupling ergodic theorems with explicit upper bounds for convergence rates for regenerative processes obtained in the first volume. These theorems are a basis for getting ergodic theorems with explicit upper bounds for convergence rates for semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation. We give the constructive definitions of a regenerative process with a transition period and thinned regenerative processes, formulate and comment on the weighting absolute continuity condition, which plays a key role in ergodic theorems with explicit upper bounds for convergence rates, and present ergodic theorems explicit power and exponential upper bounds for convergence rates for regenerative processes.