Short answer
The Quran says Allah created mankind from one soul, Adam, and created from it its mate, Hawwa (Eve). Most classical scholars, based on the hadith, understood that she was created from Adam's rib. The hadith that mention the rib use it to teach men to be gentle with women, not to make women lesser.
Sunni scholars hold that Hawwa was created from Adam, as the Quran states, and the majority took the rib literally, following the hadith. Men and women are equal in their humanity and in the reward for faith and deeds.
The four schools agree on this.
Explanation
Allah says: "O mankind, fear your Lord, who created you from one soul and created from it its mate and dispersed from both of them many men and women" (4:1). Another verse adds that He created the mate "that he might dwell in security with her" (7:189). The Quran does not use the name Hawwa; it calls her Adam's wife. The name comes from the hadith and the scholars.
The Prophet ﷺ said: "Take good care of women, for woman was created from a rib, and the most curved part of the rib is its top. If you try to straighten it you will break it, and if you leave it, it will stay curved. So take good care of women." The point of the hadith is kindness: accept your wife as she is, and do not try to force her into your own shape.
Most classical commentators took the rib literally, and reports from early authorities add that it was his left rib, taken while he slept. Some later scholars read the rib in the hadith as an image for women's nature. Both groups agree that Hawwa came from Adam, as the Quran says, and that this does not lower her rank: "Never will I allow to be lost the work of [any] worker among you, whether male or female; you are of one another" (3:195).
Read more about Prophet Adam, did Adam and Eve sin? and Women in Islam.
The evidence
Quran, Surah An-Nisaa 4:1
بِسْمِ ٱللَّهِ ٱلرَّحْمَٰنِ ٱلرَّحِيمِ يَٰٓأَيُّهَا ٱلنَّاسُ ٱتَّقُوا۟ رَبَّكُمُ ٱلَّذِى خَلَقَكُم مِّن نَّفْسٍۢ وَٰحِدَةٍۢ وَخَلَقَ مِنْهَا زَوْجَهَا وَبَثَّ مِنْهُمَا رِجَالًۭا كَثِيرًۭا وَنِسَآءًۭ ۚ وَٱتَّقُوا۟ ٱللَّهَ ٱلَّذِى تَسَآءَلُونَ بِهِۦ وَٱلْأَرْحَامَ ۚ إِنَّ ٱللَّهَ كَانَ عَلَيْكُمْ رَقِيبًۭا ﴿١﴾
O mankind, fear your Lord, who created you from one soul and created from it its mate and dispersed from both of them many men and women. And fear Allah, through whom you ask one another, and the wombs. Indeed Allah is ever, over you, an Observer.
States that Hawwa was created from Adam.
Quran, Surah Aal-i-Imraan 3:195
فَٱسْتَجَابَ لَهُمْ رَبُّهُمْ أَنِّى لَآ أُضِيعُ عَمَلَ عَٰمِلٍۢ مِّنكُم مِّن ذَكَرٍ أَوْ أُنثَىٰ ۖ بَعْضُكُم مِّنۢ بَعْضٍۢ ۖ فَٱلَّذِينَ هَاجَرُوا۟ وَأُخْرِجُوا۟ مِن دِيَٰرِهِمْ وَأُوذُوا۟ فِى سَبِيلِى وَقَٰتَلُوا۟ وَقُتِلُوا۟ لَأُكَفِّرَنَّ عَنْهُمْ سَيِّـَٔاتِهِمْ وَلَأُدْخِلَنَّهُمْ جَنَّٰتٍۢ تَجْرِى مِن تَحْتِهَا ٱلْأَنْهَٰرُ ثَوَابًۭا مِّنْ عِندِ ٱللَّهِ ۗ وَٱللَّهُ عِندَهُۥ حُسْنُ ٱلثَّوَابِ ﴿١٩٥﴾
And their Lord responded to them, "Never will I allow to be lost the work of [any] worker among you, whether male or female; you are of one another. So those who emigrated or were evicted from their homes or were harmed in My cause or fought or were killed - I will surely remove from them their misdeeds, and I will surely admit them to gardens beneath which rivers flow as reward from Allah, and Allah has with Him the best reward."
Shows men and women are equal in reward.
Sahih al-Bukhari 3331
Sahih... اسْتَوْصُوا بِالنِّسَاءِ، فَإِنَّ الْمَرْأَةَ خُلِقَتْ مِنْ ضِلَعٍ ...
"Take good care of women, for woman was created from a rib."
The hadith that mentions the rib, given as advice to treat women well.
Where the ruling is recorded
- Tafsir Ibn Kathir, Commentary on Surah al-Nisa, verse 1. Reports that Hawwa was created from Adam's rib.
- Umdat al-Qari (Badr al-Din al-Ayni), Book of the Prophets, the creation of Adam and his offspring. The Hanafi commentary explains the rib hadith.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. 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.