As you may know, the latest kernel version available is Kernel 4.20 RC3, which can be easily installed via the Ubuntu PPAs.
Installation instructions:
Because it is very difficult to compile a Linux kernel, Canonical has packed all the kernel releases as deb packages and made them available for everybody that uses Ubuntu or Ubuntu-based systems, via its kernel.ubuntu.com repository.
The below commands are available for all the Ubuntu, Linux Mint, Elementary OS and other derivative systems.
For 32 bit systems, download and install the i386 debs. For 64 bit systems, download and install the amd64 packages:
How to install Kernel 4.20 RC3 32 bit Ubuntu and derivative systems:
Download the needed packages:
$ cd /tmp
$ wget \
kernel.ubuntu.com/~kernel-ppa/mainline/v4.20-rc3/linux-headers-4.20.0-042000rc3_4.20.0-042000rc3.201811182231_all.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v4.20-rc3/linux-headers-4.20.0-042000rc3-generic_4.20.0-042000rc3.201811182231_i386.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v4.20-rc3/linux-image-4.20.0-042000rc3-generic_4.20.0-042000rc3.201811182231_i386.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v4.20-rc3/linux-modules-4.20.0-042000rc3-generic_4.20.0-042000rc3.201811182231_i386.deb
Install the Kernel:
$ sudo dpkg -i linux-headers-4.20*.deb linux-image-4.20*.deb
Optional, remove the kernel:
$ sudo apt-get remove linux-headers-4.20* linux-image-4.20*
How to install Kernel 4.20 RC3 on 64 bit Ubuntu and derivative systems:
Download the needed packages:
$ cd /tmp
$ wget \
kernel.ubuntu.com/~kernel-ppa/mainline/v4.20-rc3/linux-headers-4.20.0-042000rc3_4.20.0-042000rc3.201811182231_all.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v4.20-rc3/linux-headers-4.20.0-042000rc3-generic_4.20.0-042000rc3.201811182231_amd64.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v4.20-rc3/linux-image-unsigned-4.20.0-042000rc3-generic_4.20.0-042000rc3.201811182231_amd64.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v4.20-rc3/linux-modules-4.20.0-042000rc3-generic_4.20.0-042000rc3.201811182231_amd64.deb
Install the Kernel:
$ sudo dpkg -i linux-headers-4.20*.deb linux-image-4.20*.deb
Optional, remove the kernel:
$ sudo apt-get remove linux-headers-4.20* linux-image-4.20*