How to create a multiple category posts archive page

I would like to know how to create a single archive page that sorts posts from a bunch of categories and displays the posts in order (most recent first).

Something like:
Title of the most recent post that happens to be in category B
Excerpt (Read More)

Title of recent post that happens to be in category A
Excerpt (Read More)

Title of a less recent post in category A
Excerpt (Read More)

Title of an older post in category C
Excerpt (Read More)

etc.

Then there is pagination … page 2,3,4 etc of same above