This text covers the essentials of stochastic dynamic programming (also known as stochastic optimal control, Markov decision processes, or Markov decision chains) with a specific focus on the application of queueing theory. The text integrates both theory and computation in its discussion of stochastic dynamic programming. The theory of optimization criterion is first developed and proven before giving the computational methods to determine the numerical policies of the theory. Focusing on queueing systems allows for an in-depth exploration of the application of the outlined principles