The Linux kernel is the operating system kernel that is behind any number of operating systems in the Linux family. There are many builds coming out all the time. It is one of the largest open source projects in the world. Here is an online book about the linux kernel click here.
Greg Kroah-Hartman is one of the developers of the Linux kernel. Here is something about what he does and his general setup click here. Here he talks about the linux kernel. Its a great little incite into how the kernel is built click here.