Logicians have developed beautiful algorithmic techniques for the construction of computably enumerable sets.  This textbook presents these techniques in a unified way that should appeal to computer scientists.Specifically, the book explains, organizes, and compares various algorithmic techniques used in computability theory (which was formerly called "classical recursion theory").  This area of study has produced some of the most beautiful and subtle algorithms ever developed for any problems.  These algorithms are little-known outside of a niche within the mathematical logic...