Macromedia, the company that created Flash, has been bought by Adobe a couple of years ago, and since then there have been some new releases of Flash. The current version is Flash (Professional) CS3. There is also the Flash-based FlexBuilder 3, which has an IDE based upon Eclipse and is more targeted at coders, whereas the Flash CS3 authoring tool aims more at designers. There is also the free Flex SDK that gives you an ActionScript compiler and other command-line development tools.
Then there is Adobe AIR, which extends the Flash environment so that you can create desktop applications. And then there is Flash Remoting, which allows your Flash/ActionScript application to use server side code as if it were running locally on the client. Flash Remoting works with Java, .NET, ColdFusion, PHP, Python and a bunch of other server-side platforms. Oh, and there's also a Flash Communication server, in case you want to integrate something like video conference features into your Flash application.
The ActionScript language has now reached version 3 and has become a more sophisticated object-oriented language with a curly braces syntax. Like JavaScript, ActionScript is also based upon ECMAScript.
Colin Moock has written some of the best books about programming Flash and the ActionScript language; "ActionScript: The Definitive Guide" and "Essential ActionScript" are must-haves. Visit
http://www.moock.org/ for more info.
There are plenty of tutorials on the web - Google is your friend. But prepare yourself for a rather steep learning curve; Flash and ActionScript are harder to learn and more complex than BlitzMax, for example. And the more sophisticated development tools (FlexBuilder, Flash Pro) do not come cheap.