[Guide] How to root the Samsung Galaxy S IV (GT-I9505) using Chainfire Auto-Root

When a new smartphone comes along it has almost become customary for the dev-community to find a root for it. In some cases, you wont even have to wait for the actual device to come out, because renowned developer Chainfire has rooted the Samsung Galaxy S4 with a fully working auto-root mechanism.

[NOTE] This root method only works with the Galaxy S4 LTE GT-I9505, which is based on the Qualcomm processor.

[NOTE] While this root method comes form a renowned developer. This site will not take any responsibility for data loss or damage which can occur from using this device. Please proceed at your own risk.

[NOTE] Before you proceed make sure you have a Samsung Galaxy S4 (GT-I9505) with firmware XXUAMD2.

1. Download the following files by heading to the source link and extract them to a convenient location.
• Chainfire Auto-Root package.
• Odin3 Flash utility.
• At least 50% battery remaining on your device.
• USB drivers configures for your Galaxy S IV
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2. Place your Galaxy S4 in Download Mode using the correct button combination
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3. Launch Odin3 on your computer and connect your device to the computer while it is in Download Mode using the USB cable. Odin will detect the connection and indicate a COM port on top.
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4. Under PDA, select the .tar.md5 file that you extracted from Chainfire Auto-Root package. 
• Make sure that Re-Partition is unchecked,  
• Hit the Start button and begin the flash process
  [NOTE] Make sure you dont touch anything at this time
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5. Once the flashing is complete, the device will automatically reboot with a red Android logo, after which you will have root access.
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6. If your device boots without the red Android, manually reboot into recover to initiate the process

Your done. You can now enjoy root access on your Samsung Galaxy S IV.

source - XDA Developers