The kernel can be easily installed on a running system. During the boot process, the kernel is started with the latest version number by default. If you want to return to an old version, you can select the desired kernel version in the grub menu „Advanced options for Linux Mint“.

sudo apt install libncurses5-dev build-essential libssl-dev

Check here whether a patch is available for your currently installed kernel and download it. If not, choose the next newer version and download the patch.

For example:
If you are running a 4.4.165 kernel choose the following patch:
patch-4.4.148-rt166-rc1.patch.gz

• Clone the kernel

  git clone git://git.kernel.org/pub/scm/linux/kernel/git/stable/linux-stable.git

• Check out the same version as choosen for the patch

  git checkout -b RTPatch tags/v4.4.148

• Go into the kenrel source directory
• Applay the patch

  patch -p1 < <pathToPatch>/patch-4.4.148-rt166-rc1.patch

This selection will affect, how many modules will be built. The sizef and the range of functions of the monolitic kernel will not be changed. Additional modules can be built and installed after the kernel is installed.

• a.) Minimal: This will only build modules which are essential. Some basic function like Wifi drivers may be missing. Some basic Ethernet drive are in the monolitic part of the kernel and will still work
• b.) Full module support A normal Linux distribution, like Ubuntu, will install a kernel and most of the available kernel modules. Many of them are never used, because they are drivers for hardware, wich is not installed on the PC. This variant contains the same modules like a full Ubuntu kernel.
• c.) Only selected modules