Fundamentals of the Cycle Representations of Markov Processes -- Directed Circuits -- Genesis of Markov Chains by Circuits: The Circuit Chains -- Cycle Representations of Recurrent Denumerable Markov Chains -- Circuit Representations of Finite Recurrent Markov Chains -- Continuous Parameter Circuit Processes with Finite State Space -- Spectral Theory of Circuit Processes -- Higher-Order Circuit Processes -- Cycloid Markov Processes -- Markov Processes on Banach Spaces on Cycles -- The Cycle Measures -- Wide-Ranging Interpretations of the Cycle Representations of Markov Processes -- Applications of the Cycle Representations -- Stochastic Properties in Terms of Circuits -- Lévy’s Theorem Concerning Positiveness of Transition Probabilities -- The Rotational Theory of Markov Processes.