backing up system image before rooting: please help I have a Samsung Galaxy S III i9300. On Windows 7 there is something called a
recovery partition which contains a full compressed image of the operating system
from which Windows 7 can be installed. On Android, instead, there is a recovery,
which as I understand it is a partition with a full micro-operating system
from which can be used to decompress an operating system from an image on
the sdcard and make it the current operating system.

What I want to ask is. I want to root my device. For this, I can use Odin 3
and ChainFire. Once the device is rooted will I be able to go back and
unroot the device? In order to do so I would like to save the program
which reinstalls the android operating system from scratch. Where is
this program. I want to back it up in case needed, I don't want to
lose it or customize it.

I can see my image on sammobile.com, but the download is slow if you do not
pay for the download, and I was unable to download the image.

If I install ClockworkMod as my recovery, I need to root the device first before
installing ClockworkMod, so when ClockworkMod overwrites the recovery, the old
recovery will be gone and I will only be able to restore the rooted version of
the OS. Plus, I will not be able to reinstall the old recovery as once overwritten
by ClockworkMod this old/original recovery will be gone. Is this correct?
What if I want to back up the unrooted version of the OS?

Thanks.
First, there is no such thing as a "full copy" of the system stored anywhere on the device, as it is with the Windows recovery partition you describe. Neither is there a "program which reinstalls the android operating system from scratch" stored on the device, so you could back that up (installation is always done via rom-flashing, which takes care of itself).

Second thing is a chicken-and-egg problem: in order to create a partition-image backup, you will need root access -- so you cannot do that backup before your device is rooted (and a custom recovery is in place to provide the necessary tools). But then you no longer can backup the original state, as that has been altered by the rooting process (and custom recovery installation). So the only way to have the "real stock state" available is to download a stock image.

However, the rooting process itself is reversible (see the unrooting tag). And with a full stock installation archive (including the recovery and everything), you should be able to restore the "pre-rooting" state. Not having a Samsung device, I can however not tell about any flash-counters which would let Sammy know what "dirty work" you did in between...