Sufism was started by the Muslims in the 1st Hegira century when the companions and their tabi'in try to avoid anything that they got after they succeeded in opening Iraq, Egypt, Syria and other countries. Some of them decided to remain as the Mujahideen or busy with worshipping, serve the people by teaching or do other worthwhile activities in their lives. At that time they have been called as "Az-Zuhaad." The word "Zahid" means less favorable to the pleasures of the world due to fear that it may cause lost the time and attention to the truth, which is eternal bliss and do not make the life of this world as an ending.
After that Sufism has been developed among muslims and there were many great sufi leaders such as Abu al-Qasim Al-Junaid, Syadzily, Naqshabandy etc. The great sufi, al-Baghdadi is an example of how life should fill out in preparation for the life hereafter.
Today, Muslims in all around the world believe and accept the existence of Sufism because they knew that Sufism is part of the Sunnah and the way of life of the first four caliphs.
