In this lecture I introduce higher rank tensors formally for the first time. I first create prototypes of these objects by first defining the outer product of vectors and covectors and then figuring out how they transform under a change of coordinates. Using these transformation rules to define tensors, I then go on to talk about a few properties of tensors in general. I show how, tensors of a given rank form a linear vector space. I also introduce the notions of contraction of indices and the outer product of tensors. At the very end, I hint at a "better" coordinate-independent framework for defining tensors - but the details of this are to be discussed in the next lecture.
