The MySQL extension is deprecated and'll be removed in the future what's the reason AH solution

The MySQL extension is deprecated and'll be removed in the future, what's the reason?
I configured on my Computer 2-plan-team this system, which is written in PHP, after configuration, open index.php, but the following problems: Php Deprecated:mysql_connect (): The MySQL extension is Deprecated and would be removed in the Future:use mysqli or PDO instead in E:\SERVER\2-PLAN-TEAM\INCLUDE\CLASS.DATENBANK.P HP on line 38
Source code for class.datenbank.php:

/*
* The class Datenbank (database) provides methods to handle a database connection
*
* @author original code from Open Dynamics.
* @name Datenbank
* @version 0.4.6
* @package 2-plan
* @link http://2-plan.com
* @license http://opensource.org/licenses/gpl-license.php GNU general Public License V3 or later
*/
Class Datenbank
{

/*
* Constructor
*/
function __construct ()
{
}

/*
* Establish a database connection
*
* @param string $db Database name
* @param string $user Database user
* @param string $pass Password for database access
* @param string $host Database Host
* @return BOOL
*/
Function Connect ($db _name, $db _user, $db _pass, $db _host= "localhost")
{

Mysql
$db = new PDO ("mysql:host= $db _host;dbname= $db _name", $db _user, $db _pass);

$conn = mysql_connect ($db _host, $db _user, $db _pass);
$db _check = mysql_select_db ($db _name);
if ($db _check)
{
return true;
}
Else
{
return false;
}
}

/*
* Wrap mysql_query function

