Main references: 
Rogers, Hartley, Jr. Theory of recursive functions and effective computability. McGrawHill Book Co., New YorkToronto, Ont.London 1967 xx+482 pp.

Cooper, S. Barry Enumeration reducibility, nondeterministic computations and relative computability of partial functions. Recursion theory week (Oberwolfach, 1989), 57110, Lecture Notes in Math., 1432, Springer, Berlin, 1990.

Odifreddi, P. G. Classical recursion theory. Vol. II. Studies in Logic and the Foundations of Mathematics, 143. NorthHolland Publishing Co., Amsterdam, 1999. xvi+949 pp. 

Articles: 
Ahmad, Seema Embedding the diamond in the Sigma2 enumeration degrees. J. Symbolic Logic56 (1991), no. 1, 195212.

Andrews, Uri; Ganchev, Hristo A; Kuyper, Rutger; Lempp, Steffen; Miller, Joseph S.; Soskova, Alexnadra A.; Soskova, Mariya I. On cototality and the skip operator in the enumeration degrees, submitted

Badillo, Liliana; Harris, Charles; Soskova, Mariya I. Enumeration 1genericity in the local enumeration degrees, To appear in Notre Dame J. of Formal logic.

Calhoun, William C.; Slaman, Theodore A. The Pi 2 enumeration degrees are not dense. J. Symbolic Logic 61 (1996), no. 4, 13641379.

Casalegno, Paolo On the Tdegrees of partial functions. J. Symbolic Logic 50 (1985), no. 3, 580588.

Case, John
Enumeration reducibility and partial degrees. Ann. Math. Logic 2 1970/1971 no. 4, 419439.

Cooper, S. B.
Partial degrees and the density problem. J. Symbolic Logic 47 (1982), no. 4, 854859 (1983).

Cooper, S. B.
Partial degrees and the density problem. II. The enumeration degrees of the Sigma2 sets are dense. J. Symbolic Logic 49 (1984), no. 2, 503513.

Davis, Martin Computability and unsolvability. McGrawHill Series in Information Processing and Computers McGrawHill Book Co., Inc., New YorkTorontoLondon 1958 xxv+210 pp.

Friedberg, Richard M.; Rogers, Hartley, Jr. Reducibility and completeness for sets of integers. Z. Math. Logik Grundlagen Math. 5 1959 117125.

Gutteridge, Lance Some results on enumeration reducibility. Ph.D. thesis Simon Fraser University (Canada). 1971.

Jockusch, Carl G., Jr. . Semirecursive sets and positive reducibility. Trans. Amer. Math. Soc. 131 1968 420436.

Kent, Thomas F.; Lewis, Andrew E. M.; Sorbi, Andrea Empty intervals in the enumeration degrees. Ann. Pure Appl. Logic 163 (2012), no. 5, 567574.

Kleene, Stephen Cole Introduction to metamathematics. D. Van Nostrand Co., Inc., New York, N. Y., 1952. x+550 pp.

Lachlan, Alistair H. and Shore, Richard A. The nrea enumeration degrees are dense. Arch. Math Log 31(4) 1992 277285.

Lagemann, Jay John Tuthill Embedding theorems in the reducibility ordering of partial degrees. Ph.D. thesis, MIT, 1971 43 pp.

McEvoy, Kevin Jumps of quasiminimal enumeration degrees. J. Symbolic Logic 50 (1985), no. 3, 839848.

Myhill, John Note on degrees of partial functions. Proc. Amer. Math. Soc. 12 1961 519521.

Sasso, Leonard P., Jr. A minimal partial degree below zero prime. Proc. Amer. Math. Soc. 38 (1973), 388392.

Sasso, Leonard P., Jr. A survey of partial degree.J. Symbolic Logic 40 (1975), 130140.

Selman, Alan L. Arithmetical reducibilities. I. Z. Math. Logik Grundlagen Math. 17 (1971), 335350.

Slaman, Theodore A.; Sorbi, Andrea A note on initial segments of the enumeration degrees. J. Symb. Log. 79 (2014), no. 2, 633643.

Soskov, Ivan N. A jump inversion theorem for the enumeration jump. Arch. Math. Logic 39 (2000), no. 6, 417437.

Soskov, I. N.; Baleva, V. Regular enumerations. J. Symbolic Logic 67 (2002), no. 4, 13231343.

