[Galaxy Tab 3 General] cfendrick:
Here is what I did to install TWRP for my Galaxy Tab 3 8.0, Root, and install Super user (compatible with the SM-T310, SM-T311 and SM-T315)

As best practice I always start with these prerequisites:

1. Full or near full charge on your new Galaxy Tab 3 8.0

2. OEM USB cable

3. Connect table to PC at least once to verify they can communicate

4. Use USB 2.0 port

5. Make sure your PC has an internet connection active

6. Make sure your table has access to a wireless internet connection

7. ** I used a Windows 7 PC ** (post 2 confirms Windows 8 works with this method)

Let’s get started (Total time less than 20 minutes, but hopefully more like 5 to 10 minutes)

1. Download ODIN 3.07 from (http://xdaforums.com/attachment.php?attachmentid=1168421&d13411114315 )

a. Extract to C: root for easy navigation

2. Download Recovery TWRP from ( http://xdaforums.com/showthread.php?t=2386098 )

a. I used release 3 from http://d-h.st/bQh which was TWRP v2.6.0.0

b. Place this in the directory from 1a

3. Power off your Galaxy Tab 3 8.0

4 With the tablet off you will now restart in "Download Mode" by holding the "HOME" button, "Volume Down" and "Power" all at the same time for about 3-5 seconds till you see the Warning!! screen

5. Toggle the "Volume Up" to enter download mode.

6. Start the ODIN.exe program you downloaded from step 1.

7. Connect your tablet to your PC

a. Drivers were automatically downloaded and installed on my Windows 7 PC (took a minute or two)

b. Make sure you have you table added in ODIN by looking at the ID:COM or in the Message window it will say Added!!

8. In ODIN Select “PDA” by putting a check in the box and then navigate to the .tar file from step 2

9. Now select “START”

10. In a few minutes or less your tablet will reboot automatically

11. Power off your tablet again and access the newly installed recovery

a. To access recovery press and hold volume up and power (release the power button once the Samsung Galaxy Tab 3 splash screen is visible continuing to hold the volume up)

b. Hold volume up until you see the standard teamwin recovery screen

12. Once in Team Win Recovery select Reboot from the menu on the bottom right if you are holding your tablet upright like a portrait. Select “System”

13. Hopefully you will be prompted to install ROOT like I was

a. If so, choose that you do and follow the rest of the on screen instruction upon boot

b. I chose the TWRP install method instead of the paly store and my tablet reboot after downloading a few files

c. I verified with root checker and I was successfully rooted

14. Should this not work you can manually install using ROOT_SGT3_8.0.zip file and flash via TWRP located here (http://www.mediafire.com/download/wjye1yssb5ksbfa/ROOT_SGT3_8.0.zip )

a. Copy ROOT_SGT3_8.0.zip to your tablet (placing on the root of the tablet storage or in the Download folder is easiest)

b. Access recovery press and hold volume up and power

c. Select "Install" from the Team Win recovery menu

d. Navigate to the .zip file and select it

e. Swipe to Confirm Flash after it is done select "Reboot" and reboot "System"

15. Verify that SuperSU is installed and run any root checker from the play store if needed

16. Update SuperSu from the play store and reboot using the TWRP method if needed.

17. Congratulations you should now be done!

You should now be Rooted and have a Custom Recovery. Additionally you are now ready for any Mods or ROMs and Kernels once released and after you do a backup in recovery :)

For thoses that have any issues try the following:(thanks to Skiebs post #27)

When you get to the step to get into Odin, make sure you unchecked Auto Reboot. Hit the PDA and find your Twrp file like normal and hit Start. Wait until Odin is done loading the file, once it's done. Put it into recovery manually.

Once I did this instead of letting Odin reboot my system, it went right into twrp recovery, then I just downloaded the ROOT manually and loaded it through twrp.