Differential graded algebras(DGAs) are one of the most important objects of study in homological algebra.
These are chain complexes with an associative and unital multiplication. Examples of DGAs include cochain complexes of topological spaces equipped with the cup product.
In fact, there are interesting interactions between DGAs and stable homotopy theory. I will present these connections, and show how they can be used to classify DGAs with polynomial homology.