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Added doi and pointer to relevant sections to
Marcelo Aguilar, Samuel Gitler, Carlos Prieto, section 6 of Algebraic topology from a homotopical viewpoint, Springer (2002) (toc pdf, doi:10.1007/b97586)
(EM-spaces are constructed in section 6, the cohomology theory they represent is discussed in section 7.1, and its equivalence to singular cohomology is Corollary 12.1.20)
added the original references:
Eilenberg-MacLane spaces originate with:
{#EilenbergMacLane53I} Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, I, Annals of Mathematics Second Series, Vol. 58, No. 1 (Jul., 1953), pp. 55-106 (jstor:1969820)
{#EilenbergMacLane54II} Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, II: Methods of Computation, Annals of Mathematics Second Series, Vol. 60, No. 1 (Jul., 1954), pp. 49-139 (jstor:1969702)
{#EilenbergMacLane54III} Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, III: Operations and Obstructions, Annals of Mathematics Second Series, Vol. 60, No. 3 (Nov., 1954), pp. 513-557 (jstor:1969849)
That Eilenberg-MacLane spaces represent ordinary cohomology is due to:
Samuel Eilenberg, p. 243 of: Cohomology and Continuous Mappings, Annals of Mathematics Second Series, Vol. 41, No. 1 (Jan., 1940), pp. 231-251 (jstor:1968828)
Early review is in
It is good to have the original references and, where feasible, to have them linked.
I have added publication data and DOI to:
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