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Revised and corrected in 2017, this book is a physicists approach to interpretation of data using Markov Chain Monte Carlo (MCMC). The concepts are derived from first principles using a style of mathematics that quickly elucidates the basic ideas, sometimes with the aid of examples. Probabilistic data interpretation is a straightforward problem involving conditional probability. A prior probability distribution is essential, and examples are given. In this small book (200 pages) the reader is led from the most basic concepts of mathematical probability all the way to parallel processing algorithms for Markov Chain Monte Carlo. Fortran source code (for eigenvalue analysis of finite discrete Markov Chains, for MCMC, and for nonlinear least squares) is included with the supplementary material for this book (available online).