Deprecated: mysql_connect() mysql extension is deprecated and will be removed in the future

I have this error Deprecated: mysql_connect(): The mysql extension is deprecated and will be removed in the future: use mysqli or PDO instead in - how to solve it?
My connect.php page is:

Example

<?php

$database="my_database_name";
$mysql_user = "my_mysql_user";
$mysql_password = "1234";
$mysql_host = "localhost";
$mysql_table_prefix = "";

$success = mysql_connect ($mysql_host, $mysql_user, $mysql_password);
if (!$success)
die ("<b>Cannot connect to database, check if username, password and host are correct.</b>");
$success = mysql_select_db ($database);
if (!$success) {
print "<b>Cannot choose database, check if database name is correct.";
die();
}
?>

I have this error deprecated mysql_connect() mysql extension is deprecated how to solve it?

deprecated mysql_connect Deprecated: mysql_connect() mysql extension is deprecated and will be removed - php mysqli

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