What is the best source to learn how to use tensor operations (exterior algebra) in Mathematica?

I’m specifically interested in the TensorProduct,TensorWedge, HodgeDual and certain build in functions to do tensor arithmetic like TensorReduce, TensorExpand.

I would like to do exterior algebra calculations where I can choose to work with basis vectors as symbolic objects (and where I can choose to work without basis vectors).

To be explicit, I would like mathematica to do this input:

v = {v1, v2}; w = {w1, w2}; v\[TensorWedge]w  

desired output:

(v1 w2 - v2 v1) e1 \[TensorWedge] e2 

actual output (in normal form):

{{0, -v2 w1 + v1 w2}, {v2 w1 - v1 w2, 0}} 

If this is not possible what source gives the best advice on how to use mathematica to deal with exterior algebra related differential geometry topics ? A simple example code, video, guide or tutorial on the wolfram site would be optimal.