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This lecture covers the basic theory for continuous time Markov chains, focusing on the concepts of recurrence and transience. The instructor explains the definitions of recurrent and transient states, and their equivalence in jump chains. The lecture also discusses hitting probabilities and the minimal function satisfying certain conditions. The concepts of irreducibility, communication, and absorbing states are explored, along with the theorem stating the equivalence of recurrence and transience between continuous and jump chains.