This book provides an introduction to queueing theory and related areas, along with the basic mathematical tools needed to study such models. It covers topics such as Markov processes, renewal theory, random walks, Lévy processes, matrix-analytic methods, and change of measure. The book also discusses basic structures like the G/G/1 and G/G/s queues, Markov-modulated models, queueing networks, and models in storage, inventory, and insurance risk. The second edition includes additional material on queueing networks, matrix-analytic methods, and other topics such as Poisson's equation, the fundamental matrix, insensitivity, rare events, extreme values, Palm theory, rate conservation, Lévy processes, reflection, Skorokhod problems, Loynes's lemma, Siegmund duality, light traffic, heavy tails, the Ross conjecture, and finite buffer problems. The references have been updated, and the book is intended as a guide for further reading rather than a bibliography. The book assumes familiarity with probability theory at the level of Breiman, Chung, Durrett, or Shiryaev. It is structured into parts, with Part A focusing on simple Markovian models and Part B on general tools and methods. The book also includes appendices, notation, and conventions.This book provides an introduction to queueing theory and related areas, along with the basic mathematical tools needed to study such models. It covers topics such as Markov processes, renewal theory, random walks, Lévy processes, matrix-analytic methods, and change of measure. The book also discusses basic structures like the G/G/1 and G/G/s queues, Markov-modulated models, queueing networks, and models in storage, inventory, and insurance risk. The second edition includes additional material on queueing networks, matrix-analytic methods, and other topics such as Poisson's equation, the fundamental matrix, insensitivity, rare events, extreme values, Palm theory, rate conservation, Lévy processes, reflection, Skorokhod problems, Loynes's lemma, Siegmund duality, light traffic, heavy tails, the Ross conjecture, and finite buffer problems. The references have been updated, and the book is intended as a guide for further reading rather than a bibliography. The book assumes familiarity with probability theory at the level of Breiman, Chung, Durrett, or Shiryaev. It is structured into parts, with Part A focusing on simple Markovian models and Part B on general tools and methods. The book also includes appendices, notation, and conventions.