Qual è la differenza tra per se e by itself ?Sentiti libero di rispondere con un esempio.

They are used differently. "per se" is something like "literally" or "in fact" or "in total", and you usually use "per se" like this:

[person or thing] is not [description] per se, [clarification]

Catalonia is independent per se, but, it has many characteristics of an independent state.
Learning Spanish is not difficult per se, but, it takes a lot of time.
Maria is not a bad person per se, but she can be very aggressive when she's drunk.

You could also use it in other negative structures:

I don't agree with that per se, but I agree with some of your points.
I didn't go to Spain per se, but I did pass through the airport in Madrid.

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"by itself" is more like "solo" or "sin otra persona/cosa" etc.

Catalonia can't become independent by itself. It needs the cooperation of Spain.
Instead of learning Spanish by itself, why not learn Portuguese at the same time?
Maria's car crashed into the tree by itself. Something went wrong with the steering.