2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62235Let $X$ be a simply connected space and $\Bbb K$ be any field. The normalized singular cochains $N^*(X; {\Bbb K})$ admit a natural strongly homotopy commutative algebra structure, which induces a natural product on the Hochschild homology $HH_* N^*X$ of the space $X$. We prove that, endowed with this product, $HH_*N^*X$ is isomorphic to the cohomology algebra of the free loop space of $X$ with coefficients in $\Bbb K$. We also show how to construct a simpler Hochschild complex which allows direct computation.21 pages, to appear in TopologyAlgebraic TopologyAlgebraic GeometryK-Theory and Homology57T30, 54C35, 55S20text