Short answer
Allah is perfectly good, wise and just. Sunni creed holds that He creates everything, including what is harmful to us, but He does no wrong, and He is not pleased with sin. Evil in the world is a test with wisdom we may not see, and people choose and answer for their own deeds.
In Maturidi and Ash'ari creed Allah creates all things, including the acts of servants (37:96), while the servant chooses and earns them and is accountable. Allah wills all that happens but is pleased only with good. Out of good manners, evil is not attributed to Him in speech, as in the Prophet's ﷺ dua: "evil is not to You".
The four schools agree on this.
Explanation
Allah's names include al-Barr (the Most Kind), al-Hakim (the All-Wise) and al-Adl (the Just). Nothing He does is unjust or pointless. The question is how evil fits with that.
Sunni creed separates two things: Allah's will (iradah) and His approval (rida). Nothing happens except by His will and creation: "Allah created you and that which you do" (37:96). But He does not love disbelief or sin, and He forbids them. Imam Abu Hanifa explained in al-Fiqh al-Akbar that good deeds happen by Allah's will, love and pleasure, while sins happen by His will and decree, but not by His love or pleasure.
The Quran also teaches a manner of speaking: "What comes to you of good is from Allah, but what comes to you of evil is from yourself" (4:79), even though "all things are from Allah" (4:78). The Prophet ﷺ said in his dua, "All good is in Your hands, and evil is not to You." Evil is never something Allah does wrongly. A pain may be harm from one side and good from another, purifying sins or raising rank.
Why allow it at all? Allah "created death and life to test you as to which of you is best in deed" (67:2). Without real choice there is no real goodness, and without hardship there is no patience, courage or mercy. Much of what we call evil is what people choose. We may not see every reason, but we are told enough to trust His wisdom. See free will and qadr and does Allah test those He loves?
The evidence
Quran, Surah As-Saaffaat 37:96
وَٱللَّهُ خَلَقَكُمْ وَمَا تَعْمَلُونَ ﴿٩٦﴾
While Allah created you and that which you do?"
Allah is the Creator of all things, including people's acts.
Quran, Surah An-Nisaa 4:79
مَّآ أَصَابَكَ مِنْ حَسَنَةٍۢ فَمِنَ ٱللَّهِ ۖ وَمَآ أَصَابَكَ مِن سَيِّئَةٍۢ فَمِن نَّفْسِكَ ۚ وَأَرْسَلْنَٰكَ لِلنَّاسِ رَسُولًۭا ۚ وَكَفَىٰ بِٱللَّهِ شَهِيدًۭا ﴿٧٩﴾
What comes to you of good is from Allah, but what comes to you of evil, [O man], is from yourself. And We have sent you, [O Muhammad], to the people as a messenger, and sufficient is Allah as Witness.
Teaches attributing evil to ourselves in speech.
Quran, Surah Al-Mulk 67:2
ٱلَّذِى خَلَقَ ٱلْمَوْتَ وَٱلْحَيَوٰةَ لِيَبْلُوَكُمْ أَيُّكُمْ أَحْسَنُ عَمَلًۭا ۚ وَهُوَ ٱلْعَزِيزُ ٱلْغَفُورُ ﴿٢﴾
[He] who created death and life to test you [as to] which of you is best in deed - and He is the Exalted in Might, the Forgiving -
Hardship and choice exist as a test.
Sahih Muslim 771
Sahih... والخير كله في يديك والشر ليس إليك ...
"All good is in Your hands, and evil is not to You."
Shows the manner of not attributing evil to Allah.
Sahih Muslim 8
Sahih... وتؤمن بالقدر خيره وشره ...
"And to believe in the decree, its good and its bad."
Belief that both good and bad happen by Allah's decree is part of iman.
Where the ruling is recorded
- al-Fiqh al-Akbar (Imam Abu Hanifa), Section on the decree and the acts of servants. Distinguishes Allah's will and creation from His love and pleasure.
- Sharh al-Aqa'id al-Nasafiyya (al-Taftazani), Section on the acts of servants. Explains that Allah creates acts and the servant earns them (kasb).
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.