Android has quickly become a very important player in the mobile space. Over the past 6 years it has grown from nothing to become the leading smartphone operating system. In fact it has become the leading operating system period (Android device shipments to top 1 billion this year -- Gartner) This puts it ahead of iOS, Blackberry, Symbian and Microsoft's mobile OS as well as Windows and MacOS.
Android has a pretty interesting history as well. It started off as a company that was developing a mobile OS. In 2005, Google purchased the company and it wasn't until 2007 that anything related to the acquisition was announced. In 2007 the Open Handset Alliance was formed. It is a group of companies whose mission is "to accelerate innovation in mobile and offer consumers a richer, less expensive, and better mobile experience. Together we have developed Android, the first complete, open, and free mobile platform." The Android OS is built on top of Linux and is (almost) completely open source meaning that it can be modified and distributed freely. The Android OS itself utilizes Java but not Sun/Oracle's Java, a different implementation so that Google or whomever does not have to pay Sun royalties. The same goes for the development of Android applications
Here are 3 screen casts that I recorded walking through the download and installation of the Android Developer Tools, the downloading of additional SDK components, setting up an Android Virtual Device and developing a Hello World application.
Part 1, Downloading and installing the Android Developer Tools
Download it: GettingStartedAndroidEclipse_part1.mp4.mp4
(There is about a minute of dead air at the end of this video while the SDK components are downloading that I forgot to trim. No need to listen to it.)
Part 2, Downloading and installing the Android Developer Tools
Download it: GettingStartedAndroidEclipse_part2.mp4.mp4
Part 3, Building a "Hello World" app for Android using the ADT
Download it: GettingStartedAndroidEclipse_part3.mp4.mp4