All good muslims should make a pilgrimage to Mecca at least once in their lifetime.

Muslims who have done so may style themselves 'Al-Haj'.

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The following is an excerpt from 'Introduction to Islam' by Dr. M. Hamidullah   

Hajj literally means to travel (i.e., towards God) and it also means an effort to dominate something (the self, in this connection). Conventionally this term is translated as 'pilgrimage,' although this far from gives the exact significance of the word Hajj. This is the third of the religious duties of a Muslim. It is obligatory on every adult, man or woman, to go once in his or her lifetime to Mecca in order to perform there the great Effort for annihilating the ego (fana), i.e., assimilating one's self with the will of God. Those who do not possess the material means of travel, are exempted from it.  

The Rites of Hajj 

At the borders of the sacred territory, around Mecca, one puts off the ordinary dress, and puts on by way of a religious uniform, two sheets of cloth --a loincloth and a shoulder cover, a dress required only of men, not of women. He is bare-headed, and one tries to forget one's self during the several days of the Hajj. He goes to 'Arafat, in the suburbs of Mecca, to pass there the day in meditation. Towards evening, he returns, passes the night at Muzdalifah, and early next morning arrives in Mina which is on the outskirts of Mecca. There he passes three days, during which he lapidates Satan every morning, sacrifices a goat, pays a short visit to Ka'bah for performing the ritual sevenfold circumambulation and running between the hills of Safa and Marwah in front of the Ka'bah. 
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