Pre-requisitesAs I already said that this rooting is from un-official sources so there is always a risk of losing important docs and logs. To avoid such risk you need to back-up your phone using some android app or you can also backup your data with help of KIES tool from Samsung. I suggest you to back up your data through KIES as it comes from more relevant source. Additionally please follow all these pre-requisites. These will help you to secure your device from all kinds of threats.
How to root Galaxy S4You can root your S4 through Odin tool. For simplification, I am diving complete process in two parts. First part deals with downloads and some processes (which you need in second part) and second part belongs to some instructions which you need to give final touch to the rooting process.
PART IDownloads Download S4 Rooting Package and Odin tool to your computer system. after downloading both the files, extract them to some suitable location (better if you go with default locations) Processes (required in step2) DOWNLOAD BOOT: First turn OFF your S4 and then turn it ON while pressing and holding Vol. Down + Menu buttons together. Means first turn off your device then keep your hands/fingers on Vol Down and Menu Keys. Without removing the pressure on both the keys, turn ON your S4, it will boot you to download mode.
PART III have compiled all the Odin rooting steps in one article. You can get complete details from here. If you find any bugs/problems with this rooting guide then let me know through your comments.