MYSQL QUERY FALSE although syntax is right - php

Question

Im a beginner in PHP learning how to combine PHP with mysql. I successfully made my login page, now im making my register page. Im now in the process of checking to see if the query is TRUE before i continue to program but i keep getting "false" when i do var_dump on the query. Im checking to make sure username don't = an existing one, than i'll move on to do the same for email.
<?php
require 'main.inc.php';
if(!checkuser()){
if(isset($_POST['register'])){
//Returning the value the user put if any
$username = $_POST['username'];
$password = $_POST['password'];
$password_again = $_POST['password_again'];
$email = $_POST['email'];
//CHeck to see if the user left any blank spaces
if( !empty($username) && !empty($password) && !empty($password_again) && !empty($email)){
if($password != $password_again){
echo '<strong>Password did not match</strong>';
}
else{
//Telling PHP what we want to get
$query = "SELECT username FROM users WHERE username=$username";
//Sending out the Query
$query_run = mysql_query($query);
var_dump($query_run);
}
}
else{
echo '<strong>Please Fill Out All Forms</strong>';
}
}
?>
<form action='register.php' method='POST'>
<p><input type='text' name='username' placeholder='username' /></p>
<p><input type='password' name='password' placeholder='Password' /></p>
<p><input type='password' name='password_again' placeholder='Confirm Password' /></p>
<p><input type='text' name='email' placeholder='Email' /></p>
<p><input type='submit' name='register' value='Create Your Account' /></p>
</form>
<?php
}
else {
echo 'You are already registered';
}
?>

Answer 1

$query = "SELECT username FROM users WHERE username='$username';
use this instead...