Make a menu that lists posts by category

I am trying to build a menu which lists Posts by Category. The code below does the trick but has an unwanted side effect – code on single.php and page.php loops through all the posts on the site. Can anyone suggest another way to achieve this? I’m trying to post this code to a codebin, but am having problems so here it is for now:

• /” class=”first”>Home

<?php
$categories = get_categories();
foreach ($categories as $cat) {?>

• cat_ID; ; echo get_category_link($cat->cat_ID);?>”><?php echo $cat->name; ?>

<?php
$catID = $cat->cat_ID;
query_posts(“cat=$catID”);
while (have_posts()) : the_post();
?>
• ” rel=”bookmark” title=”Permanent Link to <?php the_title_attribute(); ?>”><?php the_title(); ?>

<?php endwhile; ?>

<?php } //end foreach ?>