How can the Linux kernel compile itself?

I don't quite understand the compiling process of the Linux kernel when I install a Linux system on my machine.

Here are some things that confused me:

1. The kernel is written in C, however how did the kernel get compiled without a compiler installed?
2. If the C compiler is installed on my machine before the kernel is compiled, how can the compiler itself get compiled without a compiler installed?

I was so confused for a couple of days, thanks for the response.