echo '<div>';
while ($row=mysql_fetch_assoc($result))
{
    if ($row['Course']!=$old_id)
    {
        $old_id=$row['Course'];
        echo '</div>
                  <div class="sectitle">'.$row['Course'].'</div>
                  <div style="width:100%;float:left">';
    }
    if ($row['Approved']==1)
    {
        $coursedate=date("M Y", strtotime($row['Submitted']));
        echo '<div class="nbutton">
            <ul>
                <li><strong><a target="_new" href="' . $row['AssignmentURL'] . '">' . $row['URL'] . '</a></strong></li>
                <li>Instructor: ' . $row['LastName'] . ', ' . $row['FirstName'] . '</li>
                <li>Book: '.$row['TextBook'].'</li>
                <li>Submitted: '.$coursedate.' </li>
            </ul>
        </div>';
    }
}
echo '</div>';

$courses=array_unique($row['Course'])
foreach ($courses as $course)
{... This is where I get lost.

$courses = array();
while ($row = mysql_fetch_assoc($result)) {
    $courses[] = $row;
}