Qur'an is the word of Allah. It is not permissible to touch the Qur'an without ablution since in the 79th verse of the surah Al-waqıa (56th surah) it is said; “(the Quran) Which none shall touch but those who are clean.” Although some commentators comment on this verse in another way, Islamic scholars have reached a consensus that touching the Qur’an without ablution is not permissible.

However, one without ablution can read Qur’an without touching it and one can recite the surahs those one knows by heart. 

If one needs to perform full ablution (ghusl), one cannot read or recite the Qur’an or cannot touch it as well. One can recite some verses and surahs like Ayatal- Kursi, Fatiha and Ikhlas with the intention of praying.

For more information, please click on the link given below

Ghusl (Major Ablution)