(The Embodiment of Justice)
The Just, The One who is entitled to do what He does.
Allah is Al-Adl (in arabic: ٱلْعَدْلُ), The one who rectifies and sets matters straight in a just and equitable manner. He always delivers absolute justice through His wisdom without failure. He gives to each what he deserves and puts everything in its proper order.
From the root ‘a-d-l which has the following classical Arabic connotations: to act justly, fairly, equitably, to adjust properly, to make even, to straighten, to rectify, to establish justice or balance. To make equal, uniform, to turn one away from something, rightly, direct, to make comfortable with what is right.
We've mentioned previously how varying scholars have different criteria for what constitutes being a name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. The name al-Adl is not recognized as an official name by scholars such as Ibn Uthaymeen, Ibn Hazm, and Ibn al-Wazir among others. As a rule of thumb, if the name contains the prefix alif lam before the name in the Qur'an, then that's a clear indication of belonging as a name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. There is no verse directly quoting al-Adl in the Qur'an.
In Sahih Muslim, "O My servants! I have forbidden dhulm (oppression) for Myself, and I have made it forbidden amongst you, so do not oppress one another."  Here Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ makes a declaration, He can do anything He pleases, but He forbids injustice for Himself. A point made to let us know that He is not unjust. Allah then commands us to uphold this standard amongst ourselves, to call out and prevent any injustice we may see.
"Indeed, Allah does not do injustice, [even] as much as an atom’s weight; while if there is a good deed, He multiplies it and gives from Himself a great reward." (Qur'an 4:40 )
And the word of your Lord has been fulfilled in truth and in justice. None can alter His words, and He is the Hearing, the Knowing. (Qur'an 6:115)
A question that requires some reflection. In recognizing Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ as just, how can we bring this virtue into our life? Can we instead of seeking confirmation or looking to proving our side as being right, can we instead seek truth? This would necessitate leaving our emotions and ego at the door. We would have to embrace our weaknesses and the possibility of being wrong. We can also expand the scope of justice to go beyond interpersonal dynamics, we can look within the individual. Are we being just to our souls, are we treatng outselves with respect, or are we oppressive to ourselves?
Abdullah ibn Amr reported: The Messenger of Allah, peace and blessings be upon him, said, “Verily, those who were just will be in the presence of Allah upon pulpits of light, near the right hand of the Merciful, the Exalted, and both of His sides are honorable. They are those who practiced justice in their judgments and with their families and in all that they did.” 
"O you who have believed, be persistently standing firm in justice, witnesses for Allah, even if it be against yourselves or parents and relatives. Whether one is rich or poor, Allah is more worthy of both. So follow not [personal] inclination, lest you not be just. And if you distort [your testimony] or refuse [to give it], then indeed Allah is ever, with what you do, Acquainted." (Qur'an 4:135)