 Historical surveys of the early development of recursive functions and computability theory are provided by Sieg (2009), Adams (2011), and Soare (2016, part V). Many of the original sources discussed in  §1  are anthologized in Davis (1965), Heijenoort (1967), and Ewald (1996). Textbook presentation of computability theory at an elementary and intermediate level include Hopcroft &amp; Ulman (1979), Cutland (1980), Davis, Sigal, &amp; Weyuker (1994), and Murawski (1999). The original textbook expositions of the material presented in  §2  and  §3  (up to the formulation of Post’s problem) include Kleene (1952), Shoenfield (1967), and Rogers (1987; first edition 1967). The structure of the many-one and Turing Degrees is presented in more advanced textbooks such as Sacks (1963a), Shoenfield (1971), Hinman (1978), Soare (1987), Cooper (2004), and Soare (2016). In addition to Shoenfield (1967, ch. 7) and Rogers (1987, ch. 16), the classic treatment of the hyperarithmetical and analytical hierarchies is Sacks (1990). Classical and effective descriptive set theory are developed in Y. Moschovakis (2009, first edition 1980) and Kechris (1995). Simpson (2009) develops connections between computability theory and Reverse Mathematics—i.e., the axiomatic study of subsystems of second-order arithmetic whose ω-models may often be characterized using computability theoretic methods. Treatment of sub-recursive hierarchies and connections to proof theory and theoretical computer science are provided by Péter (1967), Rose (1984), Clote (2002, ch. 6–7), and Schwichtenberg &amp; Wainer (2011). Many of the historical and mathematical topics surveyed in this entry are also presented in greater detail in the two volumes of Odifreddi’s Classical Recursion Theory (1989, 1999a), which contain many additional historical references.