I agree with @Byte56 that you may be better off with something a bit simpler than Android game development, however for completeness (if other people would like to know where to look):
Steps through several different aspects of development with libgdx, from setting up your project, to drawing, to GUI's, file handling, etc.
This is the blog from the developers, and each time a new feature is introduced, there is always a very well written, comprehensive discussion of how it works and why it is there in the first place.
As has been mentioned, there are several demo's you can study to see how different things are achieved (e.g. how do you integrate Box2D physics engine into your game? or how do you animate sprites?)
In addition to the game demo's which are shown above, I find it easier to look at the tests if there is a specific feature of libgdx I want to investigate. There is good coverage of most of the different features (e.g. sprite handling, physics, file handling, etc).
And finally, the usuals: http://www.google.com, http://gamedev.stackexchange.com if you have very specific things you want to find out.
I'm sure there are several other good tutorials out there, but these are the ones I stumbled across and found helpful for my recent foray into libgdx.