Singular cohomology of a space carries a natural cdga structure induced by the cup product at the level of cochains. While the cup product is a well defined operation on singular cochains, commutativity only holds after passing to cohomology due to the presence of non-trivial Steenrod operations. This fact will be the motivating example for introducing $E_\infty$ - algebras and to explain how the $E_\infty$ structure on cochains encodes this phenomenon in a precise way. Since the theory of $E_\infty$ - algebras needs the notion of operad, general recollections on the basics of operad theory will be provided.