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Computability theory (often called recursion theory) is the branch of mathematical logic and theoretical computer science that studies which problems can be solved by mechanical procedures (algorithms), how to formalize the notion of computation, and the limits of algorithmic methods. Books in this category typically develop formal models such as Turing machines, lambda calculus, and register machines; examine central concepts like decidability, undecidability, computable and computably enumerable sets, reducibility and Turing degrees; and explore key results (for example the halting problem, Rice’s theorem, and the arithmetical hierarchy), plus extensions such as relative computability, oracles, and algorithmic randomness. They range from introductory textbooks for computer scientists and mathematicians to advanced monographs and research collections for logicians, and emphasize rigorous proof techniques, examples of inherently unsolvable problems, and the conceptual foundations of what it means to compute.

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