What are the rules with reading a quran? Do you have too wear a hijab to read a quran? And are they other rules?

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It’s not wajib to wear Hijab when reading Quran so long as you are alone or with close family members. However, it’s a sign of respect be in Hijab

Other Etiquette of reading Quran:
Face the direction of Qibla
Sit humbly and respectfully
Look into the Quran while reciting ( pay maximum attention)
Be in wudhu