Error in simple INSERT INTO statement

[kows]

you have a regular bracket instead of a curved bracket on PHP_SELF. and you're also using short tags, and you shouldn't be.

<form action="<?php echo $_SERVER['PHP_SELF']; ?>" method="post">

to check whether or not the form has been submitted, you should be checking the REQUEST_METHOD and not trying to see if $_POST['submit'] is set. this is also why you're getting a notice about an undefined index. do this instead:

if($_SERVER['REQUEST_METHOD'] == "POST"){

  //form was submitted

}else{

  //form was not submitted

}