As can be seen from the widget settings, there is an option for styling hyperlinks since the aside is most likely to contain links to other pages.
The links can be styled for color, hover color and text decoration. The options for the latter are none, underline and line-through.
Links are inserted into the text box using HTML like this...
<a href="page-name.html">Link Text</a>
If the linked page is to open in a new window, use this...
<a href="page-name.html" target="_blank">Link Text</a>