This is one of the most important topics for women حجاج. First, the reassuring news: menstruation does NOT invalidate your حج or prevent you from completing it. نبی کریم (صلی اللہ علیہ وسلم) explicitly told Aisha when she began menstruating during her حج: 'Do everything that the حاجی does, except do not perform طواف around the House until you are pure.'
What you CAN do while menstruating: stand at عرفات (the most essential pillar of حج), stay at مزدلفہ, stone at جمرات, make the animal sacrifice, remain in the state of احرام, make unlimited دعا and dhikr, attend the عرفات sermon, and collect pebbles. Regarding سعی, some scholars (including the Hanbali school) permit سعی during menstruation since it does not take place inside the مسجد proper. The farewell طواف (طواف al-Wada) is completely waived for menstruating women — this is unanimous among all scholars.
The only challenge is طواف al-Ifadah, which is a pillar of حج and requires ritual purity according to the majority. Options include: (1) Wait until your period ends, purify, and perform طواف — this is the safest approach if your schedule allows. (2) The Hanafi school permits performing طواف al-Ifadah during menstruation with protection if departure cannot be delayed, but requires a camel sacrifice as penalty. (3) Consult a scholar about your specific situation.
Prevention strategy: many Muslim women use hormonal medication to delay their period during the حج days. Consult your doctor 2-3 months before departure to find a suitable option and trial it beforehand. This is permissible in Islamic law when done for a valid purpose like facilitating worship.