I am teaching myself Flex 4 and will be documenting a series of examples as I go through the process. If you have not yet heard of Adobe Flex, here is a quick overview:

• Flex is a collection of class libraries released by Adobe for the purpose of building rich internet applications
• These classes are built ontop of the existing core Flash classes, such as Event and Sprite and are referred to as the Flex SDK [1]
• Flex can also be used to build desktop applications through the use of  Adobe AIR [2]
• Adobe’s proprietary program for creating Flex applications is Flash Builder, although there are other free open source alternatives

[1] Flex SDK (Software development kit): software framework that extends the existing Flash classes and runs in the Flash Player
[2] Adobe Integrated Runtime (AIR) is a cross-platform runtime environment for desktop applications

Flex started gaining popularity around 2005/2006 with the Flex 1.5 SDK. The new Flex 4 SDK was released in March 2010 along with Flash Builder (previously called FlexBuilder).

In my examples I will be looking at a brief  introduction into the new Flash Builder IDE [3] and Flex 4 classes. Next I’ll look at migrating an application from Flex 3 to Flex 4.

[3] Integrated development environment (IDE): a program / environment consisting of a collection of tools that assist with coding and developing applications

To follow these examples I would recommend that you install a version of FlashBuilder. The full trial is valid for 60 days:
http://www.adobe.com/cfusion/tdrc/index.cfm?product=flash_builder

A free alternative for a Flex development environment is to use Eclipse with the Flex plugin:
http://www.seanhsmith.com/2010/03/29/flex-for-free-setting-up-the-flex-4-sdk-with-eclipse-ide/

Another alternative is to use your favourite code editor and compile Flex with the command line compiler:
http://flanture.blogspot.com/2010/04/running-flex-4-sdk-and-flashdevelop.html
http://www.steamed-design.com/2009/07/free-flex-ide.html

Here is a comparison between FlashDevelop and FlexBuilder. Note that it compares FlexBuilder, the predecessor of the new FlashBuilder, which has a great improvement in performance:
http://cameronellis.posterous.com/flex-4-vs-flashdevelop-3

FlashBuilder is free for students and eligible educational institutions:
http://www.adobe.com/devnet/flex/free/index.html

To wet your appetite, here are some examples of what can be done with Flex:
http://flex.org/showcase
http://flex.org/tour
http://bkflex.wordpress.com/showcase/