"Probability and Measure Theory, Second Edition" is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion. It is clear, and is presented in a readable style. Solutions to many problems presented in text. It includes solutions manual for instructors. Material which is new to the second edition on ergodic theory includes Brownian motion, and convergence theorems used in statistics. No knowledge of general topology is required, just basic analysis and metric spaces. There is efficient organization.