User authentication

I have been trying to set up a login system that directs a user to a specific page depending on their access level that is set in the database. I’m still new to PHP and the script I’ve been using keeps returning and error. I have set this up from a sample code I found, but I can’t get it to work. If anyone can see whats wrong with this code, please help me. Or if you have any suggestion on how to achieve what I need I’d love to hear them.

The errors are:
Notice: Undefined index: auth_level in c:\inetpub\wwwroot\login\Login.php on line 34

Notice: Undefined index: auth_level in c:\inetpub\wwwroot\login\Login.php on line 37

Notice: Undefined index: auth_level in c:\inetpub\wwwroot\login\Login.php on line 40

The code I’ve been using is:

<?php 

//start sessions 
ob_start(); 
session_start(); 

//ie error checking 
header("Cache-control: private"); 

//connect to database 
mysql_connect("localhost","XXX","XXX"); 
mysql_select_db("XXX") or die("could not select db"); 

$username = "";

//extract user information from database 
if ($username && $password) 
{ 

// if the user has just tried to log in 
$query = "SELECT * FROM users WHERE username='$username' AND passwd='$password' "; 
$result = mysql_query($query); 
$row = mysql_fetch_assoc($result); 

  if (mysql_num_rows($result) >0) 
  { 
    // if they are in the database register the user id 
    $_SESSION['valid_user'] = $row['username']; 
    $_SESSION['pass'] = $_POST['password']; 
    $_SESSION['auth_level'] = $row['auth_level']; 
     } 
} 

if ($_SESSION['auth_level']==1){ 
            header("Location: Menu1.php"); 
         } 
         else if($_SESSION['auth_level']==2){ 
          header("Location: Menu2.php"); 
         }
		 else if($_SESSION['auth_level']==3){ 
          header("Location: Menu3.php"); 
         }
?>