[AT&T Samsung Galaxy S II SGH-I777] jivy26:
Instructions updated based on creepyncrawly's thread found here .

1.) How to root by using DooMLoRD's Easy Rooting Toolkit. (ZergRush Exploit) (Windows)

[*]Not working for KK6 2.3.6[*]

Download the "DooMLoRD's Easy Rooting Toolkit v3.0" package from this thread and extract it to a directory on your hard drive using WinZip or a similar program.

You need to have the USB drivers for SGH-I777 installed on your computer. (It will be "Samsung USB Driver for Mobile Phones" in Control Panel\Uninstall Programs.) Download and install the latest drivers from this thread. (x86 and x64)

Both USB Debugging (Menu\Settings\Applications\Development) and Unknown Sources (Menu\Settings\Applications) should be enabled on your phone.

Increase the screen timeout on your phone to 10 minutes. (Menu\Settings\Display\Screen Timeout) Remember to set it back to a shorter interval after you are done rooting.

Connect the USB cable to the phone and the computer. Go to the directory where you extracted the package and execute "runme.bat".

The toolkit will open a command prompt window where you will see the progress of the rooting process. It takes between 5 and 10 minutes for the process to complete.

Success. You're rooted.

2.) How to root by using SuperOneClick Root. (ZergRush Exploit) (Windows, Linux and Mac OS)

[*]Not working for KK6 2.3.6[*]

Download "SuperOneClick v2.3.1 - Automatic Driver Installation" from MultiUpload and extract it to a directory on your hard drive using WinZip or a similar program.

Please go the the SuperOneClick thread and read about the tool and how to use it. For Windows XP you need to have .NET Framework v2.0 or above installed. For Mac OS and certain flavors of Linux, you need to install Mono.

I have not tested this tool. It is included here because it claims to work for Mac OS and Linux, and provides a way to use the ZergRush Exploit on those operating systems. Since I am only familiar with Windows, I will be unable to support this rooting method. For problems, try posting questions in the SuperOneClick thread linked above.

If you try SuperOneClick on Linux or Mac, please post your (success or failure) results. Thanks.

3.) How to root by flashing Entropy512's Return/Unbrick to Stock, Kernel + Rooted System Package with Modem using Odin3 One-Click Downloader (Windows)

I have prepared Odin3 One-click Downloaders for the Stock non-rooted and Stock + Root packages. Each One-click Downloader also contains the Modem. This will make flashing back to stock or flashing root in Windows easier. These were tested and flashed successfully on my device. These could be posted in the OP for convenience.

How to Use:

Download the 7 zip package. Extract the contents of the zip file to a directory on your hard disk drive.

Start the Odin3 One-Click Downloader program by double clicking on "I777UCKH7 OCD No BL.exe" or "I777UCKH7 OCD Root No BL.exe".

Now Enter Download Mode:

With the phone powered off, plug in the usb cable while holding the vol up + vol down buttons (but not the power button).

When the warning screen appears, press Volume up to continue into download mode.

In Odin, the small edit box in the upper left corner will turn yellow, and say something like [0:COM8]. The number could be different.

Click Start. Watch the progress bar advance in green while the message box in the lower area describes the steps. When the flash is finished, the top left larger edit box will turn green and say PASS! and your phone will automatically reboot.

Unplug the usb cable from you phone after it boots up. Success.

The above is from creepyncrawly, found here.

4.) How to root by flashing Entropy512's Return/Unbrick to Stock, Kernel + Rooted System Package from the command line using Heimdall (Linux and Mac OS)

Tested on Linux, should work on Mac OS

Download and install the latest version of Heimdall Command Line for your operating system from here. (Latest version 1.3.1 at this writing.)

Download Entropy512's Return/Unbrick to Stock, Kernel + Rooted System Package from here. Extract the PDA.tar file from this package to a directory on your hard disk drive, then extract the two component files from the tar - zImage and factoryfs.img.

Place zImage and factoryfs.img both in the directory where you have the Heimdall command line executable, and enter the following at the command prompt:

Code:

heimdall flash --kernel zImage --factoryfs factoryfs.img

Reboot the phone. Success. You're Rooted.