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This introductory textbook is designed for a one-semester course on queueing theory that does not require a course in stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering. Key features include an introductory chapter, which contains a historical account of the growth of queueing theory in the last 100 years; a modeling-based approach with emphasis on identification of models using topics such as collection of data and tests for stationary and independence of observations; rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics; a chapter on modeling and analysis using computational tools; modeling exercises as a motivational tool and review exercises covering background material on statistical distributions. An Introduction to Queueing Theory may be used as a textbook by first-year graduate students and upper-level undergraduate students. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research.