I suggest checking whether the university has an Ombudsman or Ombudsperson. This is a university official who helps students (and presumably non-students in this case), when there are any kinds of problems with a university. Another person to try would be the Chairperson of the German Department (or the Department where German is housed) or the undergraduate advisor/associate chairperson in that department.
If I put a book in my cart on Amazon and dropped it back out within 10 minutes, I certainly would not expect to be charged for that!
My guess is that this is probably more like the situation where you click through on Amazon for a downloadable product (say, an ebook) – and then change your mind and want to cancel the order.
It’s quite possible that the OP didn’t know what he was doing at the time, but it definitely sounds like the enrollment was fully completed before it was canceled. And given the discrepancy between the published $100 cancellation fee and the $175 charge, there’s another piece to this puzzle that hasn’t been revealed. (Perhaps downloadable course materials? )
As long as we are doing math – the introductory level German classes were shown to be 5 units. (No classes were more than 5, although there were some 4 and 3 unit classes offered) For a nonstudent, the summer course enrollment fee is $550 per unit (so $2750 for 5 units) + $385 course registration + $56 document management. All that adds up to $3191 total – not the “over 4000” the OP claims.
So perhaps at one point in this saga there were some other courses added to the cart that were not so promptly cancelled(?).