Wilhelm Ackermann, Zum Hilbertschen Aufbau der reelen Zahlen, Math. Annalen 99 (1928), pp. 118-133.
von Heijenoort. From Frege To Gödel, 1967. This is an invaluable reference in understanding the context of Ackermann's paper On Hilbert’s Construction of the Real Numbers, containing his paper as well as Hilbert’s On The Infinite and Gödel’s two papers on the completeness and consistency of mathematics.
Raphael M. Robinson, Recursion and double recursion, Bull. Amer. Math. Soc., Vol. 54, pp. 987-993.
^An inverse-Ackermann style lower bound for the online minimum spanning tree verification problem November 2002
Erich Friedman's page on Ackermann at Stetson University
Scott Aaronson, Who can name the biggest number? (1999)
Some values of the Ackermann function.
Example use of the Ackermann function as a benchmark[失效链接]. Note the huge number of function calls used in computing low values.
Decimal expansion of A(4,2)
Hyper-operations Posting on A New Kind of Science Forum discussing the arithmetic operators of the Ackermann function and their inverse operators with link to an extended article on the subject.
Robert Munafo's Versions of Ackermann's Function describes several variations on the definition of A.
"Hilbert's Program", The Stanford Encyclopedia of Philosophy (Fall 2003 Edition), Edward N. Zalta (ed.)