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This is an extended and corrected version of the First Edition. The major changes are:–Chapters 2 through 5 are now appended by lists of problems and exercises. We also provide answers and a number of solutions.–Chapter 5 includes three new sections on applications, to queueing theory, to risk, and to branching processes, and a new section describing time to exceed a high level by a random walk and its location around that time.–Sections 5.1, 5.2 and 5.9 are extended.