What webbased tools can I use to create a

I want to build a webtool that allows user to view PDFs but I also want to add
my own toolbar to allow users to do some custom things to the document like
select text and return that text to the webapp (built with AJAX). Or maybe
insert a bookmark or open multiple PDF documents in multiple windows to compare
them.

What tools do I need to build something like this???

By a web tool, do you mean an ordinary application that the user can
install which connects to the web and displays PDFs? Or something
else?

Would this be for end users who have purchased Acrobat Professional?

By "webtool" I basically mean an AJAX web application that performs a
specific function: viewing and modifying PDFs.

I need to find a way to do this so end users would NOT need to purchase
Acrobat.

I've seen it done with Flex, which means in theory it should work with AIR as
well.

However, the Acrobat SDK would be way out of range for this. You are not allowed
to install Acrobat on a web server (section 2.3 of the EULA), so it would have
to be entirely separate from the Acrobat SDK, since the SDK is nothing and does
nothing without Acrobat installed.