If you want to upgrade to Kernel 3.10, but avoid compiling it from sources or downloading the packages from kernel.org and installing it by hand, download the installation script and run it.
To install kernel 3.10 on Ubuntu 13.04 Raring Ringtail, Ubuntu 12.10 Quantal Quetzal, Ubuntu 12.04 Precise Pangolin, Linux Mint 15 Olivia, Linux Mint 14 Nadia, Linux Mint 13 Maya, Debian Sid, Debian Wheezy and Debian Squeeze.
Instructions for installing Kernel 3.10 RC1 on 32 bit Ubuntu / Debian derivates:
Download the needed packages:
$ wget -c kernel.ubuntu.com/~kernel-ppa/mainline/v3.10-rc1-saucy/linux-headers-3.10.0-031000rc1_3.10.0-031000rc1.201305130510_all.deb
$ wget -c kernel.ubuntu.com/~kernel-ppa/mainline/v3.10-rc1-saucy/linux-headers-3.10.0-031000rc1-generic_3.10.0-031000rc1.201305130510_i386.deb
$ wget -c kernel.ubuntu.com/~kernel-ppa/mainline/v3.10-rc1-saucy/linux-image-3.10.0-031000rc1-generic_3.10.0-031000rc1.201305130510_i386.deb
Install the Linux Kernel 3.10 RC1:
$ sudo dpkg -i *.deb
Instructions for installing Kernel 3.10 RC1 on 64 bit Ubuntu / Debian derivates:
Download the needed packages:
$ wget -c kernel.ubuntu.com/~kernel-ppa/mainline/v3.10-rc1-saucy/linux-headers-3.10.0-031000rc1_3.10.0-031000rc1.201305130510_all.deb
$ wget -c kernel.ubuntu.com/~kernel-ppa/mainline/v3.10-rc1-saucy/linux-headers-3.10.0-031000rc1-generic_3.10.0-031000rc1.201305130510_amd64.deb
$ wget -c kernel.ubuntu.com/~kernel-ppa/mainline/v3.10-rc1-saucy/linux-image-3.10.0-031000rc1-generic_3.10.0-031000rc1.201305130510_amd64.deb
Install the Linux Kernel 3.10 RC1:
$ sudo dpkg -i *.deb