What path to take depends entirely on what your goals are, so without knowing those, it's difficult to give much advice.
If you just want a better understanding, in order to communicate with your watchmaker, then reading a few books, learning the nomenclature, etc. will be enough.
If you want to tinker as a hobby, then there might be better ways of getting started.
If you want to repair watches for others, then that's a different thing entirely.
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