The Quran is the speech of Allah, the Divine guidance, a supreme revelation of the Lord of the universe. It’s the passport to Paradise, a shield from the fire of Hell. It describes itself as the noble book, the exalted Scripture, and treasury of Divine wisdom. No wonder it stipulates that anyone who holds it in their hands to read it must be clean, i.e must wash by performing the Islamic ritual of Wudu (ablution). Therefore, it is not permissible for a Muslim to touch the Arabic Quran when they don’t have wudu, according to the majority of scholars.
This is the view of the four imams (Hanafi, Malaki, Shafi, Hanbali) and this was the view expressed by the companions of the Prophet (peace be upon him). The same applies to moving the Quran from place to place if the person who is moving it is not in the state of Wudu. But if they touch it or move it with something in between, such as picking it up in a wrapper, then it is acceptable. But if they touch it directly, this is not permitted according to the view of the majority of scholars.
The Quran can be recited from memory if the person is without wudu, or for them to read it if the Quran is held by someone who has wudu.
So, read the Arabic Quran in state of cleanliness, in Wudu. However, Quran translations without the Arabic like ‘The Majestic Quran’ paperback edition do not require Wudu. According to some scholars (the Malaki Jurists) book or a translation and commentary of the Quran that has less than 50% Arabic can be read without Wudu.
The wisdom behind cleaning oneself before touching the Divine book is a clear statement of respect for the book, belief in its wonderful Divine nature. Its physical preparation for a spiritual journey.