[Xiaomi Redmi Note 3 Questions & Answers] kuba3351:
So, if you unlocked your bootloader using OFFICIAL METHOD (got approval for unlocking and downloaded MI Unlock Tool), next thing you have to do is replacing your stock recovery with a TWRP, because on stock recovery, you are unable to flash any custom ROM.

Follow this if you are on the newest MIUI available and no more updates in the Updater app:

Download this one: https://www.androidfilehost.com/?fid=24727332921017084

After that, unpack the zip file on your computer. Next, power off your phone, and switch it on in FASTBOOT MODE (like you did while using Mi Unlock tool), and connect phone into your computer.

Start the flash.bat script. Follow the instructions it displays. After that, your phone will be rebooted into RECOVERY mode. If recovery start in Chinese language, you can switch it to English, this is described in this thread: https://xdaforums.com/redmi-note-3/how-to/zcx-twrp-install-twrp-flash-supersu-t3462448

After you will get a working custom recovery, with language that you understand, THE FIRST THING YOU HAVE TO DO IS BACKUP EVERYTHING YOU HAVE BEFORE PLAYING WITH ANYTHING. This recovery is able to make a backup. So, ckick on Backup option, and select EVERYTHING to backup. If you have an external SD card, switch the location from internal memory into the external SD card. Then swipe to begin backup process and wait until it finish.

After that, you have to decide whitch custom ROM to flash.

If you want to get high stability, and no extra features, you should choose this:

https://xdaforums.com/redmi-note-3/development/rom-t3612905

If you want a lot of extra features, but less stability, choose this:

https://xdaforums.com/redmi-note-3/development/rom-resurrectionremix-5-8-0-t3507433

If you want a good stability and some extra features, choose one of this:

https://xdaforums.com/redmi-note-3/development/rom-pure-nexus-substratum-fi-wifi-t3577060

https://xdaforums.com/redmi-note-3/development/rom-nitrogen-os-11-01-2017-t3536211

https://xdaforums.com/redmi-note-3/development/rom-viperos-t3613688

https://xdaforums.com/redmi-note-3/development/rom-aospextended-rom-v1-2-t3506955

All these ROMS are based on the newest released android, 7 Nougat. You can also try another ROMS in the SNAPDRAGON development section,

How to flash a ROM:

Download the zip file contains a rom, and place it in the SD card in to your phone or the internal memory.

Run your phone in the recovery mode. To do it switch it off, and turn it on by pressing Volume UP + Power. Check if you see your backup in the Restore section. If yes you will be able to restore it if something will go wrong.

Reset your phone into factory settings by selecting Wipe Data and swipe. After that go into the Install Zip section, and choose your zip contains the ROM. Swipe to flash it. After flash complete, use wipe Cache/ Dalvik cache option, and select "Reboot System". Your phone should boot up and load your custom ROM intead of MIUI. You will notice that there is no Google Play and another Google Services. It is not bundled with ROM due to Google licensing policy. If you want to have it, Google "Open Gapps", download it, and flash the zip in recovery mode like before, but don't wipe anything this time. After flashing done, boot up your ROM again and you will have a Google Play and another things from Google.