… gleaned from Baha’i literature

During His youthful years Bahá'u'lláh reproved the behavior of a famous religious leader for showing disrespect towards Christ

In a gathering where Bahá'u'lláh was present a famous high-ranking Sufi religious leader who was highly esteemed by Muhammad Shah, was holding forth on the station that a human being can attain. Referring to himself, he said, 'Should my servant come to me and say that Jesus the Christ was at the door, asking for me, my detachment is such that I would express no wish to see Him.' Some of those present kept silent, while others out of flattery murmured assent. Only Bahá'u'lláh spoke up. He turned to the boastful divine who had expressed such disrespect for a Manifestation of God, and said: 'You are very close to the person of the sovereign and he is very devoted to you, but if the chief executioner with ten of his men were to come to this door and tell you that the monarch wanted to see you, would you take it calmly or would you be perturbed?' The arrogant religious leader paused for a while before replying, 'In truth, I would feel anxious.' 'In that case,' said Bahá'u'lláh, 'you should not make such an assertion.'

Bahá'u'lláh's authoritative statement left them all speechless.
(Adapted from “Baha’u’llah, the King of Glory’, by H.M. Balyuzi; from an account by Mirza Abu’l-Fadl)

A mujtahid’s dream about Bahá'u'lláh during His youthful years – recalled by ‘Abdu’l-Baha

'Abdu'l-Baha has described how His own grandmother, who lived in Yalrud (a village near Takur) went one day at dawn to the house of a famous mujtahid to pray. This mujtahid (a doctor of Islamic law) was a distant relative of the family. After the morning prayer he told ‘Abdu’l-Baha’s grandmother that he had some excellent news for her. He had had a dream in which he had found himself outside a house which no one was allowed to enter, because, said the door-keeper, within it the Qa'im of the House of Muhammad (the Promised One of Shi’ih Muslims) was closeted with Mirza Husayn-'Ali of Nur [Bahá'u'lláh]. At first the mujtahid had expressed his surprise that the son of a vizier should be so privileged; but on remembering their distant kinship, he had ascribed the privilege to this fact.
(Adapted from ‘Bahá'u'lláh, The King of Glory’, by H.M. Balyuzi)

An example of Bahá'u'lláh’s great soundness of judgement and insight as a youth

In the village of Yalrud which is near Bahá'u'lláh’s ancestral home in Takur, in northern Iran, there lived a mujtahid by the name of Shaykh Muhammad-Taqi who was well-famed throughout the land. He had a thousand scholars of divinity around him, whom he taught and, from time to time, presented with a complex question to resolve.

Whenever Bahá'u'lláh returned to His home in Takur, He would usually stop for a while in Yalrud, and here He would visit the mujtahid, who was distantly related to His family.

During a visit to Yarud, when Bahá'u'lláh was sitting in the company of Shaykh Muhmmmad-Taqi and other scholars and divines, He was asked to resolve a question they had been unable to answer to the mujtahid's satisfaction.

The problem was this:

From Childhood Baha’u’llah was “gifted in every way, and adorned with purity and nobility”

…There was in Ṭihrán… a Youth of the family of one of the ministers and of noble lineage, gifted in every way, and adorned with purity and nobility. Although He combined lofty lineage with high connection, and although His ancestors were men of note in Persia and universally sought after, yet He was not of a race of doctors or a family of scholars. Now this Youth was from His earliest adolescence celebrated amongst those of the ministerial class, both relatives and strangers, for single-mindedness, and was from childhood pointed out as remarkable for sagacity, and held in regard in the eyes of the wise. He did not, however, after the fashion of His ancestors, desire elevation to lofty ranks nor seek advancement to splendid but transient positions. His extreme aptitude was nevertheless admitted by all, and His excessive acuteness and intelligence were universally avowed. In the eyes of the common folk He enjoyed a wonderful esteem, and in all gatherings and assemblies He had a marvelous speech and delivery. Notwithstanding lack of instruction and education such was the keenness of His penetration and the readiness of His apprehension that when during His youthful prime He appeared in assemblies where questions of divinity and points of metaphysic were being discussed, and, in presence of a great concourse of doctors and scholars loosed His tongue, all those present were amazed, accounting this as a sort of prodigy beyond the discernment natural to the human race. From His early years He was the hope of His kindred and the unique one of His family and race, nay, their refuge and shelter.
- ‘Abdu’l-Baha  (‘A Traveler’s Narrative’)

Bahá'u'lláh became renowned for His learning when He was about thirteen years old

He was extremely kind and generous. He was a great lover of outdoor life, most of His time being spent in the garden or the fields. He had an extraordinary power of attraction, which was felt by all. People always crowded around Him, Ministers and people of the Court would surround Him, and the children also were devoted to Him. When He was only thirteen or fourteen years old He became renowned for His learning. He would converse on any subject and solve any problem presented to Him. In large gatherings He would discuss matters with the 'Ulama (leading mullas) and would explain intricate religious questions. All of them used to listen to Him with the greatest interest.
- 'Abdu'l-Baha  (Quoted by Esslemont in ‘Baha'u'llah and New Era’)

Bahá'u'lláh didn’t attend any schools

The education and instruction which Bahá'u'lláh received was limited both in nature and extent, as He Himself states in the Tablet addressed to Nasir’d-Din Shah: 'The learning current amongst men I studied not; their schools I entered not. Ask of the city wherein I dwelt, that thou mayest be well assured that I am not of them who speak falsely.'

In those days, the scions of noble houses were taught such matters as befitted their station in life, such as riding, handling a gun, wielding a sword, calligraphy, acquaintance with the works of the great classical poets of the land, a good reading knowledge of the Holy Book, the Qur'an, and hardly ever anything more. They were given such instruction by tutors, specially engaged by the parents, who were also required to teach them good manners.
- Balyuzi  (‘Bahá'u'lláh, The King of Glory’)

Bahá'u'lláh’s father had an amazing dream about his Son

Baha'u'llah's father
When Bahá'u'lláh was still a child, the Vazir, His father, dreamed a dream. Bahá'u'lláh appeared to him swimming in a vast, limitless ocean. His body shone upon the waters with a radiance that illumined the sea. Around His head, which could distinctly be seen above the waters, there radiated, in all directions, His long, jet-black locks, floating in great profusion above the waves. As he dreamed, a multitude of fishes gathered round Him, each holding fast to the extremity of one hair. Fascinated by the effulgence of His face, they followed Him in whatever direction He swam. Great as was their number, and however firmly they clung to His locks, not one single hair seemed to have been detached from His head, nor did the least injury affect His person. Free and unrestrained, He moved above the waters and they all followed Him.

The Vazir, greatly impressed by this dream, summoned a soothsayer, who had achieved fame in that region, and asked him to interpret it for him. This man, as if inspired by a premonition of the future glory of Bahá'u'lláh, declared: "The limitless ocean that you have seen in your dream, O Vazir, is none other than the world of being. Single-handed and alone, your son will achieve supreme ascendancy over it. Wherever He may please, He will proceed unhindered. No one will resist His march, no one will hinder His progress. The multitude of fishes signifies the turmoil which He will arouse amidst the peoples and kindreds of the earth. Around Him will they gather, and to Him will they cling. Assured of the unfailing protection of the Almighty, this tumult will never harm His person, nor will His loneliness upon the sea of life endanger His safety."

As a boy Baha’u’llah was amazed at pointless discourses by some clerics

Baha'u'llah ... records that on one occasion, when visiting his future mother-in-law, he listened to a cleric with a large turban expounding on whether the arch-angel Gabriel was the greater or Qanbar, the servant of the Imam ‘Ali. He writes that although he was still but a boy, he was astonished at the ignorance of these elders and when an opportunity came, he expressed his thoughts saying that since Gabriel is stated in Qur’an to be the one through whom the Word of God is revealed to the prophet Muhammad, then even Qanbar's master the Imam ‘Ali would not reach that station. Baha'u'llah states that some time later, he visited Qum and was dismayed to find the same cleric expounding the same sort of pointless and fruitless discourse.
- Moojan Momen  ('Baha’u’llah, A Short Biography')

While in still a child, Baha’u’llah sought the dismissal of an unjust and tyrannical tax-collector

While still a child, the Blessed Beauty watched as a government tax-collector, on three separate occasions, accosted His father and demanded, in a cruel and unjust manner, the payment of taxes. Unable to bear the injustice of it all, He, though in early childhood, mounted His horse and rode for two days until He arrived in Tihran. There, He sought the dismissal of this unjust and tyrannical tax-collector. He succeeded in obtaining the necessary papers ordering the dismissal, and returned to His parents.
- 'Abdu'l-Baha (Words of 'Abdu'l-Baha recorded by Dr. Diya Baghdadidi, unpublished Memoirs; in 'Stories of Baha’u’llah', compiled by Ali-Akbar Furutan)

His short stature when seven years old

When Baha’u'llah was seven years old, one day His mother was watching the elegance of His bearing as He paced to and fro, and remarked 'He is somewhat short of stature.' but His father answered: 'It is of no importance. Are you not aware of His capacity and His abilities? Such intelligence! And such perception! He is as a flame of fire. Even at this young age He surpasses mature men.' Whenever difficult problems were discussed and no one seemed able to resolve them, the youthful Blessed Beauty would provide the solution.
- ‘Abdu’l-Baha  (Quoted by Ishraq-Khavari in Risaliy-i-Ayyam-i-Tis’ih p. 67; in 'Stories of Baha’u’llah', compiled by Ali-Akbar Furutan)

A Child with extraordinary powers of intellect, wisdom and innate knowledge - singled out among His siblings by relatives and family friends

From His earliest childhood Baha’u’llah was singled out among His siblings by relatives and family friends, whose composite opinion was that the Child had extraordinary powers of intellect, wisdom and innate knowledge, and was superior to others of his age and class. A common prediction applied to the little Baha’u’llah in that superstitious age of high child mortality was that 'such a precocious Child will not survive!' [1], for it was anticipated that child prodigies were especially fated to suffer early doom. All who encountered Him in those years of boyhood admitted that he was gifted in every way, and in addition was adorned with a rare purity and nobility. [2] 
- David Ruhe  (‘Robe of Light’)
[1] 'Abdu'l-Baha, quoted in Star of the West, Vol. 3, NO.9, p. 3 (1912)
[2] 'Abdu'l-Baha, ‘A Traveler's Narrative

Dreams at the age of five or six

At the age of five or six the Blessed Beauty had a dream which He described to His father. In the dream He found Himself in a garden. Huge birds were attacking Him from every side, but were unable to inflict any harm. He then went to the sea and, as He was swimming, the birds of the air and the fish of the sea attacked Him, but He was not harmed. His father summoned a famous seer to interpret the dream. 'This dream-indicates', replied the seer, 'that the Child shall be the founder of a great Cause, and that all the leaders and learned men throughout the world will attack Him, but, like the birds and the fish, they shall do no harm. He will be victorious over all.’
- ‘Abdu’l-Baha  (Quoted by Ishraq-Khavari in Risaliy-i-Ayyam-i-Tis’ih p. 65; in ‘Stories of Baha’u’llah’, compiled by Ali-Akbar Furutan)

"This Child never cries"

The mother of the Blessed Beauty was so enthralled with Him that she could not contain her amazement at His behaviour. 'This Child never cries,' she would say; 'He is so unlike other babies who cry and scream and are forever restless while in the nursing stage . . .'
- ‘Abdu’l-Baha  (Quoted by Ishraq-Khavari in Risaliy-i-Ayyam-i-Tis’ih p. 62; in ‘Stories of Baha’u’llah’, compiled by Ali-Akbar Furutan)