What does Islam teach about child marriage?

In Surah 2:228, Allah says through Muhammad that a man has to wait three of his wife's monthly cycles before he can divorce her, setting precedent for the Islamically righteous means of divorce. In Surah 65:4, it gives additional rules for exceptions; when women are too old, too young or pregnant. This is confirmed in the tafsirs of Ibn Kathir, Al-Jalalayn, Ibn Abbas and others; showing marrying young children who haven't yes reached puberty was allowed, hence divorce rules needed to be made.

In Sahih al-Bukhari 5133, the chapter heading is given as 'Giving one's young children in marriage', before going on to discuss Muhammad marriage and consummation with Aisha, quoting Surah 65:4 in the chapter. This well established fact is also covered in Sahih al-Bukhari 5133, 5158, Sahih Muslim 3481, 3482 and Sunan Abi Dawud 2121; unanimously repeating marriage at six and consummation at nine.

Aisha was also prepubescent upon consummation. In Sahih Muslim 3481, when she was taken to consummate the marriage, she was playing with dolls (images, which are forbidden for those past puberty). Prepubescents were the only females allowed to have dolls because they weren't morally accountable; all explained in detail and this context with this very example in Sahih al-Bukhari 6130.