What are the types of ablution (wudu'), and is it necessary to have the intention for prayer with every ablution, or is the intention to remove ritual impurity sufficient for the prayer to be valid with it?

Ablution (wudu') is divided into obligatory for prayer and sunnah (recommended) for various matters. Al-Mahamili mentioned ten types of recommended ablution, while others added to them, reaching twenty-five types. These include: renewing ablution, ablution during ghusl (ritual bath), before sleeping, before eating for a person in a state of janabah (major ritual impurity), after carrying a deceased person, when angry, after backbiting, for reciting the Qur'an and Hadith, for studying sacred knowledge, for the call to prayer (adhan) and the iqamah, for delivering a sermon (other than the Friday sermon), for visiting the Prophet's grave, for standing at Arafat, for performing sa'i (ritual circumambulation between Safa and Marwa), after phlebotomy (venesection), cupping, vomiting, and eating camel meat (to avoid dispute regarding its obligation), for every sleep or touch that is disputed as a nullifier, for touching a hermaphrodite, and for trimming the mustache.

If a person performs ablution for a recommended reason, such as reciting the Qur'an, it is not sufficient for them to pray the obligatory prayer with it, according to the Maliki school and most Shafi'is. This is because the act intended is valid even if ritual impurity remains, so the intention did not include lifting the impurity. It is recommended for a Muslim to always be in a state of purity, and it is permissible to perform ablution before the time for prayer begins. For the intention of ablution, it is sufficient to intend to lift ritual impurity, or to make prayer permissible, or to perform the obligation. It is not necessary to bring to mind the intention of prayer with every ablution. Whoever intends to lift ritual impurity during ablution (whether the ablution is obligatory or recommended) may pray and circumambulate the Kaaba with it. As for whoever intends an action that does not require ritual purity (such as reciting the Qur'an), the aforementioned details apply.