Dear @doxdrum, thank you for your reply.
I was thinking about somethign like this:
https://cadabra.science/notebooks/beginners.html
(this is the first tutorial on the official website: finding the equations of motion for the Faraday field $F_{\mu \nu}$ by varying the action).
How about adding a complementary turorial where one derived the equations of motion for the complex scalar Klein-Gordon field? In this way, one can learn how to deal with complex fields and (at the same time) scalars: in fact, I see quite good references for vectors (i.e. $A^\mu$), spinors and, of course, the metric and higher rank tensors (since Cadabra seems to be very General Relativity oriented).
To be specific, it would be amazing to have a tutorial on these lines:
https://en.wikipedia.org/wiki/Klein–Gordon_equation#Lagrangian_formulation
Since the compelx Klein-Gordon has a conserved U(1) charge, this tutorial would be extremely useful, a fort of first step for everyone interested in checking the conserved quantities of an action with the Noether theorem. Thank you again!