Login Page validation

Hello dear
How are you....?
I'm Shujaat form Pakistan
here is complete solution of your problem

save this code with page name: connect.inc.php

<?php					//To connect script with database
$mysql_host = 'localhost';
$mysql_user = 'root';
$mysql_pass = '';

$mysql_db = 'a_database';

if(!mysql_connect($mysql_host, $mysql_user, $mysql_pass) || ! mysql_select_db($mysql_db)){
  die(mysql_error());
}  
?>

Save this page with name: core.inc.php

<?php
ob_start();     //ob_start should start before use of header function, which is to     redirect our user back to index page when they login correctly
session_start();	 //session_start should initialize before we use session

$current_file = $_SERVER['SCRIPT_NAME'];	//{'SCRIPT_NAME'} tell us what is current page
$http_referer = $_SERVER['HTTP_REFERER'];

//function to check weather session is empty or not?
function loggedin(){	
  if(isset($_SESSION['user_id']) && !empty($_SESSION['user_id'])){
    return true;
    }else{
          return false;
          }
}

      function getUserField($field){
        $query = "SELECT $field FROM users WHERE id = '".$_SESSION['user_id']."' ";
        if($query_run = mysql_query($query)){
          if($query_result = mysql_result($query_run, 0 , $field)){
            return $query_result;
          }else{
            echo 'Love.';
          }
        }
      }
?>

save this page with name: loginform.inc.php

<?php
//this should not userequire 'core.inc.php';
require_once('core.inc.php');	

//cheching login form is empty or not? And then form data send to database server to compare weather data is valid or not? After that start session if data is valid.
if(isset($_POST['username']) && isset($_POST['password'])){
  $username=$_POST['username'];
  $password=$_POST['password'];
  $password_hash = md5($password);				//converting data to md5

  if(!empty($username) && ! empty($password)){
//here we select id form table rather username, so that we can access whole data of a user who logged in
    $query = "SELECT id FROM users WHERE username = '".mysql_real_escape_string($username)."' AND password = '".mysql_real_escape_string($password_hash)."'";
    if($query_run = mysql_query($query)){
      $query_num_rows = mysql_num_rows($query_run);
      if($query_num_rows==0){
        echo 'Invalid';
      }else if($query_num_rows ==1){
      //mysql_result have take these three arguments, 
      //$query, The result resource that is being evaluated. This result comes from a call to mysql_query().
      //Then Row(0) The row number from the result that's being retrieved. Row numbers start at 0.
      //third one is "field" The name or offset of the field being retrieved. It can be the field's offset, the field's name, or the field's table dot field name (tablename.fieldname). If the column name has been aliased ('select foo as bar from...'), use the alias instead of the column name. If undefined, the first field is retrieved.

      $user_id = mysql_result($query_run, 0, 'id');
        echo $user_id;
        $_SESSION['user_id']=$user_id;		//starting session and assigning user id to recognize user
        header('Location: main.php');		//header return user to main.php page
      }
    }
  }else{
    echo 'You must enter a username and password.';
  }
}
?>
<form action="<?php echo $current_file; //variable recognize current page of website  ?>" method="POST">		
Usrename: <input type="text" name="username">
Password: <input type="password" name="password">
          <input type="submit" value="Log in">
</form>

save this page with name: logout.php

<?php
require 'core.inc.php';
           
session_destroy();

header('Location:'.$http_referer);
?>

save this page with name: main.php

<?php
require 'core.inc.php';			//calling other page which has some function of login part
require 'connect.inc.php';		//calling other page which has some function of login part

//loggedin function is declare in core.inc.php page to check that weather session is exist or not and session is continue or not?

if(loggedin()){
  $firstName = getUserField('firstname');
  $surName   = getUserField('surname');

  echo 'Welcome '.$firstName.' '.$surName.'...!<br> You are login. <a href = "logout.php">LogOut</a><br>';

}else{
  include 'loginform.inc.php';
}
?>

save this page with name: register.php

<?php
require 'core.inc.php';
require 'connect.inc.php';
if(!loggedin()){

  if(
     isset($_POST['username']) &&
     isset($_POST['password']) &&
     isset($_POST['password_again']) &&
     isset($_POST['firstname']) &&
     isset($_POST['surname'])
  ){

     $username       = $_POST['username'];
     $password       = $_POST['password'];
     $password_hash  = md5($password);
     $password_again = $_POST['password_again'];
     $firstname      = $_POST['firstname'];
     $surname        = $_POST['surname'];

         if(
            !empty ($username) &&
            !empty ($password) &&
            !empty ($password_again) &&
            !empty ($firstname) &&
            !empty ($surname)
         ){

              if($password == $password_again){
                $query = "SELECT username FROM users WHERE username = '$username'";
                $query_run = mysql_query($query);


                  if(mysql_num_rows($query_run)==1){
                    echo 'Sorry..! This user name '.$username.' already exist. <br>Please try with any other.';
                  }else{
                    $query = "INSERT INTO users VALUES ('', '$username', '$password_hash', '$firstname', '$surname')";
                      
                      if($query_run = mysql_query($query)){
                        header('Location: register_success.php');
                      }
                  }


              }else{
                echo 'Password is not matching.<br> Please enter again same password.';
              }

         }else{
           echo 'All fields are required. Thanks';
         }



  }

?>
<form action="register.php" method="POST">
Username:<br>   <input type ="text" name="username" value = "<?php echo $username; ?>"><br><br>
Password:<br>   <input type ="password" name="password"><br><br>
Password Again: <br> <input type="password" name="password_again"><br><br>
First Name:<br> <input type="text" name="firstname" value = "<?php echo $firstname; ?>"><br><br>
Sur Name:<br>   <input type="text" name="surname" value = "<?php echo $surname; ?>"><br><br>
                <input type="submit" value="Register" >
</form>

<?php
}else if(loggedin()){
  echo 'You\'re logged in.';
}
?>

save this page with register_success.php
You are register

now this is complete solution of your problem.
Take care
&
Best of Luck

Thank You very much Shujaat .. i really appreciate your effort on helping me .. i'm gonna review this one for awhile .. coz i don't wanna pass the exam without understanding it ..

again THX .. :)