I would like to write a small C program which starts a Mathematica session, executes some user defined code and retrieves the output and finally quits the session. Basically I like to have a simple custom made user interface for Mathematica based on standard C. I am confident that such libraries exist since I am using a program of this kind for Maple (based on OpenMaple libraries). I just do not know where to start. Maybe somebody can point me to the documentation. Ideal would be a small sample application. Maybe something like this ships with Mathematica?
Don't be confused by the comments. Eventhough the answer "see the Documentation" seems obvious here (as I ask for it), the by far best resource for the solution is on the Wolfram webpage. See also my answer below. As far as I can see it is neither referenced in the documentation nor contained in the builtin examples. Not knowing the words to search for it took some effort to find it.