Assuming you have Category Arhiving enabled, check out something like this, to get you started.
CODE
<MTArchiveList archive_type="Category">
<b> <MTArchiveCategory></b><br>
<MTEntries>
<MTEntryDate>: <a href="<MTEntryPermalink>" title="<MTEntryExcerpt>"><MTEntryTitle></a><br />
</MTEntries>
<br /><br/>
</MTArchiveList>
That lists the entry title, linked to the archive page, for each entry in each of the categories. If you want to display the full text of some or all of the posts for each category, you'd just need to change the code within the MTEntries tags to reflect what you want to show for each category.

Post back if you have more questions, or if I've misunderstood your request!