Can I build the Ubuntu Kernel? I heard that the Ubuntu kernel is a special version of the linux kernel.
Ubuntu Linux kernels are open source and are available for downloading and building.
For each Linux kernel version they maintain Ubuntu kernel developers maintain a set of patches until those patches are incorporated upstream. They also maintain a specific configuration. When you install a Linux image package the configuration used to build it is stored in /boot along with a map file, the kernel image, and an initrd file created for your system at the time the linux image package is installed.
This is a wiki page that describes the current maintained kernels source location. Each is stored in a git repository. As Clepto mentioned in his answer, https://help.ubuntu.com/community/Kernel/Compile contains instructions on how to get the soruce and do the compile. You can also compile vanilla kernels using an Ubuntu config, or your own config.
The Kernel development team also maintains packages for current upstream kernels in case you simply want to test one of those. That's useful for some bug testing. You can read more here.
Finally it should be possible to do a straight kernel
Needless to say, Ubuntu developers can't support a vanilla mainline kernel or one you compile yourself.
The standard Linux open source license applies, GPL V2.
I think this will help you https://help.ubuntu.com/community/Kernel/Compile/