[OS X Emacs] emacs Latex word/expression auto-completion

[wishi]

Hi fellows!

I'm writing lots of math-stuff at the moment, in LaTeX. Auctex in
Aquamacs emacs (pre-installed) comes in very handy. But what I'm
missing, being not a really sophisticated emacs user: where's something
like Tab-Completion for Latex (or other) expressions? Sometimes they are
really long ;).
I got to know emacs can everything. Well... ;) Can I complete words,
just like an IDE can, hitting Tab?
If someone knows a nifty default option I can put in my .emacs to enable
that by default - would be great.

Another question: If I want to create a Tab, to format my source-code a
little better, emacs resists doing that. I don't know... seems to be a
little wired having 20 matrices. Is there any option to make that
possible, too?

Thanks in advance,
wishi