Reguar expression - what with *

Hi,
I have a little problem with understanding of regular expression. I
read chapter from "Introduction to automata theory..." and I don't get
it couple of things.
1. I have a regular expr. like this: (( a+b )a* )* and I'm trying to
describe it, and it's like this in my opinion: at the very beginning
language generated by this regular expr. has 'a' or 'b' and then
multiple of 'a' (empty, a, aa...). And now my question what about the
last '*' sign? How to write it down?
2. I.m trying to find regular expression which generates languages
where in word i cannot have 'bbb' (there can be ...bb... or ..b...b...
or ...b...). So far I have something like this a*+ (a*ba*) + (a*bba*) +
(a*ba*ba*). Is it true or there is something missing?

BIG thx for any answers, clues etc.

Regards,
Pi

.

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