Displaying Category Titles

I currently have 3 categories set up. One I have directed to its own page, and the other 2 I want displayed on my main post page. I was able to exclude the 3rd category from the main page, but I am having some difficulty displaying the Category Titles.

On the main blog page I would like to display the excerpts of 2 Categories. The way I would like them displayed is as follows:

<h1> Category Title 1

Excerpt
<read more>

Excerpt
<read more>

…etc.

<h1> Category Title 2

Excerpt
<read more>

Excerpt
<read more>

…etc.

Any help on how to display the category titles this way?

All comments are appreciated.