Table Of Contents / Post Index Sorted By Category

Hello Everyone –

I need to have a table of contents type of deal on my main blog page. I have been trying to come up with this for a while now but I keep getting the category title above each and every post, not grouped like I am trying do to.

CATEGORY NAME (#1)
Post Title
Post Title
Post Title…

CATEGORY NAME (#2)
Post Title
Post Title…

Can anyone share some code on how to do this? I have clearly hit a wall in my thinking.

My current code:

<?php if (have_posts()) : while (have_posts()) : the_post();
  if( $post->ID == $do_not_duplicate ) continue; update_post_caches($posts); ?>

<h3 style="margin-left:30px; padding-bottom:5px;"><?php the_category(' '); ?></h3>

<h4 class="index" style="margin-left:60px;"><a href="<?php the_permalink() ?>"><?php the_title() ?></a></h1>

<?php endwhile; ?>