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The purpose of this text is to provide the reader with a solid background and understanding of the basic results and methods in probability theory before entering into more advanced courses. The first six chapters focus on the central areas of probability: multivariate random variables; conditioning; transforms; order variables; the multivariate normal distribution; and convergence. The final chapter discusses the Poisson process as a means to both introduce stochastic processes and to apply many of the techniques introduced earlier in the text. Students are assumed to have taken a course in probability though no knowledge of measure theory is required, the text is supplemented by many examples.