The download you provided is listed as the r8169 driver. The Realtek r8169 module is provided by the default linux kernel (it's pre-installed).
First, run the following command to check if the module is in use:
lsmod | grep r816
If the module is listed, you are done. Use the next step to list your devices. If the module is not listed, proceed to the next step and then continue.
Next, run the following command to list your current devices:
ifconfig -a
Then, use the following commands to enable the kernel module (driver) and to list your devices:
sudo modprobe r8169
ifconfig -a
Finally, you should see an additional ethernet device listed.
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METHOD 2:
Use the following method if the default driver doesn't work:
If you have problems with the kernel module, you can download the driver directly from Realtek.
Click here to visit the website
Select "GBE Ethernet LINUX driver r8169 for kernel up to 5.6" to download.
Then, install the dependencies:
sudo apt update
sudo apt install build-essential linux-headers-generic linux-headers-$(uname -r)
Next, cd
into the same directory as the download and then run the following commands:
mkdir r8169
cd r8169
tar xvf ../r8169*bz2 --strip-components 1
If you get a "not found" error for the following command, just ignore and proceed.
sudo modprobe -r r8169
sudo make clean modules
sudo make install
sudo depmod -a
sudo modprobe r8169
Check to see if the module is loaded:
lsmod | grep r8169
List your devices:
ifconfig -a
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The drawback of installing the driver manually is that you will have to reinstall the driver after any future kernel update.
Otherwise, you will need to use the following instructions to manually update the driver.
After you boot up using a new kernel, cd
back into your r8169 directory and then run the following commands:
sudo modprobe -r r8169
sudo make clean
sudo make clean modules
sudo make install
sudo depmod -a
sudo modprobe r8169
However, as mentioned by @Terrance, you can avoid this problem by converting the driver to DKMS which will automatically install during future updates.
When following the instructions, don't forget to use the corresponding driver name r8169 and also the correct version number of your downloaded driver.