Question: Are there any existing languages where the programmer can change the language's syntax at any point? 

That means one can write the language in the syntax one likes, and there is some translator to translate it back to some "standard code", which can be compiled or interpreted.

The code will also be readable, because "standard code" can be translated to the version of code another coder likes. 

I had this question because some people might like the design of a language, but doesn't like the syntax. (for example, Lisp with [] instead of (), Lisp with f(x) instead of (f x)).

Also, it be nice if anyone can provide some academic sources on topics like this.

Edit: I found one, [FreeForm](http://freeformlang.sourceforge.net/).

Answer: 
In the specific case of Lisp:

* Lisp has macros! You can transform the language in any way you please using Lisp macros.
* You can also create reader macros to change the way source expressions are parsed in Lisp.
* For more extensive changes to the source format, you can even make your own reader. See David A. Wheeler's [readable S-expressions](http://www.dwheeler.com/readable/) proposal for an example.
There's various things that lean in that direction... But I suspect my list will suffer from the "Oh no, that's not magic at all!" syndrome.

But...

* The C Preprocessor
* Code reformatters (to make code indented the way you prefer, or
whatever)
* Operator overloading
* Various language precompilers, like the Coffeescript-to-Javascript in
Rails 3.1