Abstract: Suppose we have a space with a multiplication that is not strictly associative, so $(xy)z$ and $x(yz)$ are not equal. If we want to multiply $n$ elements together, we now have many ways to do so depending on where we choose to put our parentheses. Often we have some additional data, such as paths between $(xy)z$ and $x(yz)$ and some coherency between these paths, and we would like to keep track of this data to see how to relate the different ways of multiplying $n$ elements. Operads provide a concise way of encoding this type of data of operations and relations between them. In this talk I will define operads and give examples that determine to what extent a multiplication is associative or commutative up to homotopy. In particular, I will discuss $E_n$-operads and their relationship to $n$-fold loop spaces.