In which language is the C# compiler written?

I looked at the source code at http://referencesource.microsoft.com/, and it appears all the source code is in C#.

I also looked at the source code for the new C# compiler platform (Roslyn), and it is also in C#. How is that possible? Is C# language compiler written in C#? Or am I missing something obvious? If C# compiler is written in C# then how does it work?

The original C# compiler wasn't written in C#, it was in C and C++. The new Roslyn compiler was written in C#, but was initially compiled with the old compiler. Once the new compiler was done, it was able to compile its own source code: this is called bootstrapping.

Compilers are utility programs - they turn programming language text into machine code. If the programming language describes software that just happens to be a compiler.....

Compilers can also produce machine code for other architectures. For example, Apple compiles iOS using racks of Intel-based servers. The compiler does not have to run the ARM code it generates, just write it to disk.

Compiler 2.0 must be written in a language compiler 1.0 can process, but it can certainly create compiler 2.0 with newer features like optimization. You can then re-compile the source code using compiler 2.0 and make a better version of itself. Again, the compiler doesn't know it's making another version of itself.

If we go far enough back into the mists of time then we do reach a point where we have no compiler - the very first iteration of a high-level language. Then we have to get out the pencils and opcode books and write the first one in assembly. How did we write the first assembler? Direct machine code entry, probably on punched paper tape, or flipping switches on the front panel.