I am currently reading Cartan semináire on Algebraic Topology, especially homology groups of Eilenberg-Maclane spaces. Cartan has developed a magnificient machine to compute homology groups of these space by mean of the so-called the bar construction in arbitrary coefficients; unlike his student, Serre, who used spectral sequences but these tools just work for $\mathbb{Z}_2$ coefficient.
In this lecture, Cartan wrote that Maclane, in his paper, Eilenberg-MacLane, Ann. of Math. 58, 1953, p.55-106, proved that there is an isomorphism
$$H_{\star}(\overline{\mathfrak{B}}^{(n)}(\Lambda G)) \cong H_{\star}(K(G,n),\Lambda)$$
where $\Lambda,G,\Lambda G$ are a commutative ring with unity, an abelian group and the group ring, and $\mathfrak{\overline{B}}^{(n)}$ is the iterative bar construction. The problem of computing $H_{\star}(K(G,n))$ is therefore reduced to a purely algebraic problem. Cartan's series of lectures stress to the computational techniques rather than the aforementioned isomorphism, and MacLance's paper is written in a very old language and in my opinion, the presentation is quite difficult to me to absorb. Consequently, I would like to ask for any modern treatment of the isomorphism above, thank you in advance.