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Is there any way to easily incorporate the Linux drivers without using the Linux Kernel?

The main goal here is to use the Linux drivers to be able to use my network card etc.
Writing my OS is a learning project but my focus is on data processing and not on writing drivers.
Or is there another elegant solution?

Thank you!

Nope. The Linux driver API is generally unstable, so even if you were to emulate the relevant parts of the API, it would go out of date before you'd get much of a benefit. If you want to just steal code and adapt it, you'd have to GPL any changes and not link directly against them. If all you want is a few simple drivers, you are much better off writing them yourself.

Or copy them from other hobby OSes, which tend to keep drivers and driver interfaces simple and are often more liberally licensed.

And of course, I have to mention CDI (code, documentation) here.