Help with custom category listing

I am trying to list all the categories on my archives page (so not in the loop) and I am no PHP person. I tried this:

<?php
	foreach((get_the_category()) as $category) {
		echo '<li><a href="/topics/' . $category->category_nicename . '">' . $category->cat_name . '</a><span class="amount" style="width:"' . $category->category_count . 'px"">&nbsp;</span></li>';
	}
?>

but that only listed one category so then I read a bunch and decided I needed to probably write SQl outright so I tried this.

$categories = mysql_query("SELECT term_id FROM terms ORDER BY ID");
for($i=1;$i<($categories[$i]);$i++){
	echo '<li><a href="/topics/' . $category[$i]->category_nicename . '">' . $category->cat_name . '</a><span class="amount" style="width:' . $category->category_count . 'px">&nbsp;</span></li>';
}

That doesn’t do anything. I am just guessing here cause I have no idea with php. Can someone help me achieve what I want? I want the result of the first code sample but all the categories, not just one.