Here are the various OS X systems that can be installed on your iMac.
Mac OS X 10.0 (Cheetah) went to 10.0.4
Mac OS X 10.1 (Puma) went to 10.1.5
Mac OS X 10.2 (Jaguar) went to 10.2.8
Mac OS X 10.3 (Panther) went to 10.3.9
Mac OS X 10.4 (Tiger) went to 10.4.11
Each one of these OSs was a paid upgrade and you can't download the base system, but you can download (free from Apple) updates to the base system to get to the final version. If you want to install Tiger, you must buy the base install DVD.
Tiger install DVDs are in short supply. Tiger is no longer available at the Apple Store but may be available for $129 by calling Apple Phone Sales @ 1-800-MY-APPLE (1-800-692-7753). For other sources, do a Google search for
MA453Z/A (10.4.6),
MA190Z/A (10.4.3) and
M9639Z/A (10.4) . Also look on eBay. Be sure & buy a retail version (black with silver X)

and not a model specific version (gray) (See
Can I use another Mac's system restore disc on my Mac? ). Expect to pay (possibly a lot) more than the Apple list price of $129.
Also check these web stores:
http://www.lacomputercompany.com/cgi-bin/rpcart/index.cgi?command=dispitem&type= sku&sku=19521
http://www.allmac.com/shop/index.php?cPath=5_10003
After you install the base 10.4.x, update to the final Tiger version 10.4.11. Here's the link for the 10.4.11 combo update
http://support.apple.com/kb/TA24901?viewlocale=en_US
Look at this link
Mac OS X v10.4 Tiger Installing Software Support Page
http://www.apple.com/support/tiger/install/
You can also download the
Tiger Installation and Setup Guide
http://manuals.info.apple.com/en/TigerInstall_SetupGuide.pdf
When you upgrade the OS, do it via Archive & Install. See
About the Archive and Install feature
http://support.apple.com/kb/HT1710
Be sure to select Preserve Users & Settings. Also, repair permissions before and after the install.
 Cheers, Tom 😉
