<style>
table { border: 1px solid black; width: 100%; }
td, th {border: 1px solid black;width: 50%;}
</style>
| Image | Image Links |
|-------------------------|--------------------------------------------------------|
| <img src="image1.png"/> | *[Image1 link1][1]<br> *[Image1 Link2][2] |
| <img src="image2.png"/> | <ul><li>Image2 Link1</li><li>Image2 Link2</li></ul> |
In general, table implementations in Markdown tend to be fairly simplistic. I'm not aware of any that support Markdown-style lists inside tables.
As a result, I believe you'll have to use HTML for your table:
table {
border: 1px solid black;
width: 100%;
}
td, th {
border: 1px solid black;
width: 50%;
}
<table>
<thead>
<tr>
<th>Image</th>
<th>Image Links</th>
</tr>
</thead>
<tbody>
<tr>
<td><img src="http://placekitten.com/200/100"></td>
<td>
<!-- this _might_ work, but I'd use an HTML image even if it does -->
<ul>
<li>[Image1 link1][1]</li>
<li>[Image1 Link2][2]</li>
</ul>
</td>
</tr>
<tr>
<td><img src="http://placekitten.com/200/100"></td>
<td>
<ul>
<li><a href="">Image2 Link1</a></li>
<li><a href="">Image2 Link2</a></li>
</ul>
</td>
</tr>
</tbody>
</table>