This textbook is designed as a standalone introduction to measure theory and also provides a comprehensive treatment of integration on locally compact Hausdorff spaces, analytical and Borel sets in Polish spaces, as well as Haar measure on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, along with brief discussions of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of lifts. Measure theory offers a solid foundation for the study of functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and analysis, and the appendices provide a thorough review of the essential background material.