How To Upgrade Linux Kernel
The easiest way to do this is to install one of the supplied Linux kernel image packages on your system. They may be obtained using apt-get or aptitude if you want to use the command line, or Synaptic if you want to use a GUI.
To install a Linux kernel image, you first have to decide which one you want to use. Start with
apt-cache search linux-image
Note that images are available for several flavours - depending on your architecture.
A good overview on available versions can also be seen at linux.
The latest version can be installed using:
$ sudo apt install linux-image-<flavour>
Make sure you read everything it tells you during the installation, especially about initrd image. If you use an unusual boot loader, you might need to reconfigure after installing the image - don't forget to tell it to use appropriate initrd image for the kernel in this case (PackageManagement page has details about listing contents of a package).
There are some alternative repositories for images, but they aren't supported, and don't receive security updates (in a timely fashion):
$ sudo -i # cat >> /etc/apt/preferences.d/linux-kernel << EOF Package: * Pin: release o=Debian,a=experimental Pin-Priority: 102 EOF # apt policy # shows/verifies the current preferences # echo "deb http://deb.debian.org/debian experimental main" >> /etc/apt/sources.list # apt update # apt -t experimental install linux-image-3.10-rc5-686-pae
You might want to use unstable instead of experimental and/or choose a different mirror and flavour. Also the version and ABI version are probably different for you.
This might have some further dependencies, but generally they should not affect your stable (or testing) system. You still can select the old version in your bootloader afterwards.