What is the wisdom behind the acts of 'Umrah and Hajj, their order, and what is their purpose?

Hajj and Umrah demonstrate the Oneness and sincerity of God and establish the remembrance of God in all their rituals. Religious and worldly benefits accrue to pilgrims, those performing Umrah, and the people of the Haram, such as the gathering of Muslims, concordance in appearance and purpose, and the magnification of God's شعائر (sacred rites/symbols). The order of the acts of Hajj and Umrah carries apparent wisdom. Every act begins with the state of Ihram and the Talbiyah, then the circumambulation (Tawaf) and the striving (Sa'i), then staying overnight in Mina and standing at Arafat, and the stoning of the Jamarat, offering the sacrifice, and shaving the head, and the farewell circumambulation (Tawaf al-Wada'). The wisdom behind some actions, such as not wearing tailored clothing, is a reminder of the Day of Judgment and humility. Kissing the Black Stone is an act of worship and emulation of the Prophet, peace and blessings be upon him. The striving between Safa and Marwah reminds one of humanity's need and poverty before its Creator, and the stoning of the Jamarat symbolizes enmity towards Satan. Some functions of Hajj are considered to have details whose meanings are not readily apparent, but they were legislated as a test of the servants' obedience to their Lord. Striving to contemplate the remembrances of God and magnify His شعائر (sacred rites/symbols) are among the most important objectives of Hajj.