In  this talk, we will begin by discussing application of functions on paths, and the transport lemma (Lemma 2.3.1 of the book). We will then discuss the notion of homotopies, and equivalences, with a few examples. From their we will be able to define a function which will be called “idtoeqv”. Roughly, this function takes equality of types to equivalence of types. This will allow us to state the univalence axiom. If time permits, we will end with how the various type forming constructions behave in the presence of the higher groupoid structure.