In this lecture I take another look at tensors - and see them as simply maps that take in a bunch of vectors and covectors and return a number, linearly in each argument. I then go on to show how the components of a tensor follow naturally from its action on basis covectors and basis vectors. The transformation laws that were integral parts of the definition of a tensor in the so called "physicist's definition" now become a simple consequence of the way in which basis vectors transform. On the way, I also discuss the dual vector space and its basis - since that is essential to the discussion of how tensors transform.
