There is a general belief that Adi Shankara was initiated into Kriya Yoga by Mahavatar babaji who is said to be living in the Himalayas. But do we have any authentic reference from our ancient texts for it? Does Adi Shankara himself talk about Kriya Yoga for realizing Brahman?
The reference of Babaji giving initiation to Adi Shankara is found in Autobiography of a Yogi. As per Paramahansa Yogananda, Mahavatar Babaji himself stated that he gave initiation to Adi Shankara.
Autobiography of a Yogi / Chapter 33 - Babaji, the Yogi-Christ of Modern India:
Babaji’s mission in India has been to assist prophets in carrying out their special dispensations. He thus qualifies for the scriptural classification of Mahavatar (Great Avatar). He has stated that he gave yoga initiation to Shankara, ancient founder of the Swami Order.
Though the initiation was not of Kriya Yoga as mentioned by Paramahansa Yogananda.
Autobiography of a Yogi / Chapter 26 - The Science of Kriya Yoga:
Kriya is an ancient science. Lahiri Mahasaya received it from his guru, Babaji, who rediscovered and clarified the technique after it had been lost in the Dark Ages. "The Kriya Yoga which I am giving to the world through you in this nineteenth century", Babaji told Lahiri Mahasaya, "is a revival of the same science which Krishna gave, millenniums ago, to Arjuna."
From the above, it is clear that Babaji indeed initiated Adi Shankara but not in Kriya Yoga as the knowledge of Kriya Yoga was first given by Babaji to Lahiri Mahasaya and not Adi Shankara.
Regarding Babaji Maharaj, late Satyacharan Lahiri, the grandson of Yogiraj Shyamacharan Lahiri writes:
We do not get any information about Babaji (the Guru of Yogiraj) from the sayings and diaries of Lahiri Mahasaya (Yogiraj)..Many people have been creating imaginary stories about Him, probably to become famous. They in this way are in fact demeaning that great Krishna-like incarnation. (Foreward of Puranapurusha Yogiraj Shyamacharan Lahiri by Ashoke Kumar Chattopadhyay.)
If Sri Lahiri's grandson, who himself was a yogi knew almost nothing about Babaji, who else would know it? I just think every such information about Babaji has to be taken with a grain of salt.