What is a silsila, the unbroken chain of teachers in Sufism?

The true Tasawwuf has to be learnt and practised under the guidance of someone who has learnt and received it from another shaykh, linking the chain back to the Companions and ultimately to Allah's Last Prophet ﷺ. The Companions followed the Prophet ﷺ in every aspect, whether external or internal, and continued the Prophetic mission of Yuzakkihim, meaning "to purify them", so they became the guiding stars for the next generation of Muslims and the chain continued. [Keller, Sea without Shore] Only by following the ones who are linked to the chain can one reach the ultimate goal, which is the love of Allah.

As for the learning of Fiqh, Islamic jurisprudence, we seek knowledge from those with traditional Islamic education who are followers of one of the four Sunni schools of Fiqh: Hanafi, Maliki, Shafi'i or Hanbali. While university degrees, acclaim and published work are great achievements, they cannot replace the learning from an unbroken line of teachers extending back to the Beloved Prophet ﷺ. The same goes for Tasawwuf, as the matters of the soul and the heart are beyond the capacity of the human brain to comprehend.

Therefore, in Tasawwuf a guide is needed who has done the journey under the guidance of another shaykh from an unbroken line of teachers extending up to the Beloved Prophet ﷺ. For a bodily disease or ailment, one would never consult a self-proclaimed doctor who has read a few books on medicine, so how can one consider receiving any benefit on the spiritual path of Tasawwuf from a person who is a self-proclaimed Sufi?

Those who claim to be Sufis without a lineage of teachers up to the Beloved Prophet ﷺ are pretenders, as Tasawwuf is a discipline like any other discipline of religion and the source of all religious knowledge is the Prophet ﷺ.

Among the basic conditions for a true shaykh is public authorisation by a true shaykh, which connects him to the Prophet ﷺ through an unbroken chain of authorisation. [Keller, Sea without Shore 271]

In Tasawwuf, bay'ah is an oath taken to the path of ihsan, with the connection of the heart to the shaykh and of the soul to the Awliya of the chain back to the Prophet ﷺ. A seeker must pray that Allah raise the spiritual degrees of all the Mashaikh of the silsila. [al-Buzaydi, The Adab of the True Seeker]