(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 each what he deserves and puts everything in its proper order.
From the root ayn-dal-lam (ع د ل), 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.
Innal laaha laa yazlimu misqaala zarratinw wa in taku hasanatany yudaa’ifhaa wa yu’ti mil ladunhu ajran ‘azeemaa
"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)
Innal laaha ya’muru bil ‘adli wal ihsaani wa eetaaa’i zil qurbaa wa yanhaa ‘anil fahshaaa’i wal munkari walbagh-i’ ya’izukum la’allakum tazakkaroon
"Indeed, Allah orders justice and good conduct and giving to relatives and forbids immorality and bad conduct and oppression. He admonishes you that perhaps you will be reminded." — (Qur'an 16:90)
Wa tammat Kalimatu Rabbika sidqanw wa ‘adlaa; laa mubaddila li Kalimaatih; wa Huwas Samee’ul ‘Aleem
"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 for reflection. In recognizing Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ as just, how can we bring this virtue into our life? Instead of seeking confirmation or looking to prove 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, treating ourselves 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.” 
Yaa aiyuhal lazeena aamanoo koonoo qawwa ameena bilqisti shuhadaaa’a lillaahi wa law ‘alaa anfusikum awil waalidaini wal aqrabeen iny yakun ghaniyyan aw faqeeran fallaahu awlaa bihimaa falaaa tattabi’ul hawaaa an ta’diloo; wa in talwooo aw tu’ridoo fa innal laaha kaana bimaa ta’maloona Khabeera
"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)