With this lens auto focus?

I read something about some lenses not auto focusing with the Nikon D5100 but I was thinking about getting this lens with my kit lens, http://www.jessops.com/online.store/products/50317/show.html
but I can't really spend more than £200 on the extra lens but I would like it to be able to auto focus. Though that's not a huge problem,

I'm new to all this photography stuff.

Added (1). Will this lens***

Of course it will.

ANY of the Nikkor AF-S lenses will work with your fine camera.

Here is a link to all the rest of the Nikkor lenses made at this time

http://www.nikonusa.com/...index.page