Retrieving user information from database - help

Right, my code that I have written will retrieve the records from the database table containing the users
but I only want to display the details of the user logged in rather than all of the users.

I can't seem to work out how to change it so it only displays the logged in user.

<?php
include("database.php");

$query = "SELECT * FROM user ";
$result = mysql_query($query);
$num = mysql_num_rows ($result);
mysql_close();

if ($num > 0 ) {
$i=0;
while ($i < $num) {
$FirstName = mysql_result($result,$i,"FirstName");
$Surname = mysql_result($result,$i,"Surname");
$DOB = mysql_result($result,$i,"DOB");
$City = mysql_result($result,$i,"City");
$Postcode = mysql_result($result,$i,"Postcode");
$WebAddress = mysql_result($result,$i,"WebAddress");
$USER_ID = mysql_result($result,$i,"USER_ID");

echo "<b>First Name:</b> $FirstName<br>";
echo "<b>Surname:</b> $Surname<br>";
echo "<b>Date of Birth:</b> $DOB<br>";
echo "<b>City:</b> $City<br>";
echo "<b>Postcode:</b> $Postcode<br>";
echo "<b>Website:</b> $WebAddress<br>";
echo "<a href=\"account_save.php?id=$USER_ID\">Update</a>";
echo "<br><br>";

++$i; } } else { echo "The database is empty"; }

?>

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Your help is much appreciated.
Thank you.