WordPress auto-generates an excerpt based on the first part of your content. It strips out HTML (links, formatting, line breaks, etc.) when doing this.
You can manually specify an excerpt using the Excerpt box when adding/editing a post. If the Excerpt box doesn’t show, click Screen Options at the top-right to enable it. You can use HTML in the excerpt box.
Another approach that is often easier is to use the “More” Tag.
You may also want to try the Advanced Excerpt plugin which prevents WordPress from removing formatting when using automatic Excerpts.