The propounder of Advait Vedanta philosophy, Bhagvadpad Shankar was born on Vaishakh sud 5, 788 CE in Kaladi, a village in Kerala. His father, Shivaguru, was a Nambudri Brahmin, and mother was named Aryamba. Prior to Shankar's birth, the childless couple fervently prayed to Shiv in a mandir at Tirucchur. Shiv blessed the couple that he himself would be born as their son. Hence the child was named Shankar.
From birth Shankar exhibited astounding intelligence. By the age of two he studied the Purans and other texts. At the age of five he was given yagnopavit sanskar (janoi), and sent to study at the guru's ashram. By the age of eight he had studied the Vedas and other scriptures. Noting the boy's ascetic inclination, his mother decided to arrange an early marriage. However, Shankar, not the least interested in mundane life, requested her permission to become an ascetic. She refused, saying that there was nobody except him to look after her. Shankar respected her decision, yet yearned to become an ascetic and embark on his mission to save Sanatan Dharma. One morning soon after, when both went to bathe in the nearby Churna river, a crocodile grabbed his leg. He cried out to his mother that if she willingly gave permission for his sannyas, the crocodile would release him. Horrified at the thought of him being killed in such a hideous manner, she reluctantly granted the permission. The crocodile instantly released him.
He then set off in search of a true guru. After meeting many sadhus, he arrived at the cave of Bhagvadpad Govind, disciple of the famous Gaudapad, on the banks of the Narmada. Shankar stood at the entrance of his cave. When Govindpad opened his eyes after returning from samadhi, he asked the child, "Who are you?"
Shankar respectfully replied by composing 10 Sanskrit aphorisms. Their essential import was, "I am not the earth, nor water, nor fire, nor wind, nor space. I am chidanandrup Shiv; I am pure consciousness - the atma."
Delighted with the reply, Govindpad initiated him as his disciple. When Shankar requested a diksha mantra, Govindpad imparted four mantras, one from each Veda:

• from Rg Veda: Pragnãnam Brahma – knowledge is Brahma,
  
• from Yajur Veda: Aham brahmãsmi – I am Brahma,
  
• from Sam Veda: Tattvamasi – you are that Brahma
  
• and from Atharva Veda: Ayamãtmã Brahma – this atma is Brahma.

After imparting him wisdom, Govindpad commanded him to go to Kashi to write commentaries on the Prasthanatrayi - Brahma Sutras, Upanishads and Gita. This he accomplished at the remarkably young age of sixteen. Attracted by his supreme scriptural erudition, countless sanyasis became his disciples. Of these, four were prominent: Sanand, Mandanmishra (Sureshwar), Totakacharya and Hastamalak.
Once in Kashi, on his way to the Vishwanath mandir for Mahadev's darshan, Shankar politely requested a raggedly dressed chandal (low caste man) with four dogs to move aside. The man replied whether he should move the body or the atma? "If it is the body, your body and mine are of the same composition, of flesh, blood and bones. If it is the atma, then the atma is the same in everyone." This reply startled Shankar. He realised that this man was none other than Shiv himself and the four dogs were the four Vedas. He prostrated instantly. He expressed his divine experience - sakshatkar - of Vishwanath by composing a pentad verse known as Manish Panchakam. When he raised his head, the chandal and the dogs had vanished!
On another occasion, on the banks of Ganga in Kashi, Shankar heard a scholar vociferously repeating a grammatical rule. He advised the pundit that on his death, the rule would not help him. It would be wiser to chant the holy name of Govind. Shankar versified this (in 31 verses) in the famed melodious and devotional kirtan known as 'Mohamudgara', with the opening stanza: Bhaj Govindam... i.e. "Worship Govind, worship Govind, worship Govind, O fool! When the appointed time (death) arrives, grammar rules surely will not save you." 'Grammar rules' signifies mundane knowledge and possessions and 'bhaj' means service - offering love and devotion to God by total surrender. This essentially means navdha bhakti. In the Vivekchudamani (verse 31) he also says that among the ways of moksha, bhakti holds the supreme position:
Mokshakãranasãmagrayãm bhaktireva-gareeyasi.
Shankar's total life works of stotras and commentaries amount to about ninety, the prominent being: Saundaryalahari, Vivekchudamani, Shivanandlahari, Govindashtak, Vishnusahasranam Bhashya, etc. In the famous Gurvashtakam Stotras he emphatically advocates one to surrender to a true guru to attain Brahmapad - God-realisation. In eight verses he declares that: health, wealth, women, fame, power, material pleasures, donations or being sinless, all amount to nought if one does not accept refuge of a God-realised guru.

Consolidating Sanatan Dharma
During his short lifespan of 32, Shankar unflaggingly travelled throughout Bharat, at least twice. In all the principal sacred places he debated and defeated Shaiv, Vaishnav, Shakta and Vama Marg pundits who had propagated falsities about Vedic injunctions and deities and misguided people onto the path of sensual pleasures. In addition to these debates, by his commentaries, he also defeated the Buddhist and Jain pundits whose corrupt practices and shunyavad had nearly choked the Sanatan Dharma's pristine ideals and glory. With supreme logic and erudition he outwitted the deluded.
By his incessant travels, debates and teachings throughout Bharat, he re-united Bharat's people, saving them from ignorance, superstition, blind faith and fanaticism. To ensure that his efforts survived over the ages, he established four monastic orders in the four corners of Bharat; Jyotir Math in Badri-Kedar (north), Govardhan Pith at Jagannath Puri (east), Shrungeri Math at Shrungeri (south) and Sharda Pith at Dwarka (west). The head of each is also known as Shankaracharya. This tradition established by Adi (first) Shankar is so firm that 1200 years of tumult and foreign incursions have not dented it. On the contrary it flourishes vibrantly.

Shankar's Philosophy And Bhagwan Swaminarayan

Shankar's Advait Vedanta - non dualism (or absolute monism) - believes that this world is an illusion (maya); only Brahma is the ultimate Reality and the jiva is not different from Brahma:
Brahma satyam jaganmithyã jivo brahmaiva nãparaha.
Shankar believes in jivan-mukti, achieved solely by knowledge - gnan marg - when the jiva realises: "I am He." 'He' denotes Brahma - the highest Reality.
Unlike Shankar, who believes in only one reality, Bhagwan Swaminarayan believes in five eternal realities: jiva, ishwar, maya, Brahma and Parabrahma. His philosophy is known as Navya-Vishishtadvait - neo-qualified dualism. He also accepts jivan-mukti, in which the jiva becomes brahmarup (aksharrup) by association with the manifest form of Aksharbrahma. The liberated jiva, known as akshar mukta, then offers bhakti to Parabrahma-Purushottam - the supreme Reality. The mukta does not become Aksharbrahma, nor merges with him. Additionally, the Swami-sevak relationship always prevails between the Purushottam and mukta and between Purushottam and Aksharbrahma.
In Vachanamrut Gadhada I-42, Shriji Maharaj summarises Shankar's philosophy and highlights its true import by clarifying misinterpretations of later scholars. He says that Vedantists regard the moral do's and don'ts (vidhi and nishedh), swarg and narak, disciples who attain them and the guru, as false. However, Shankaracharya commanded his disciples to keep a staff and a gourd, to recite the Gita, Vishnusahasranam, to perform Vishnu's pujan, for the young to respect the elders, and to beg alms from pious Brahmins.
Shankar's principle that 'There is only Brahma and besides that everything including, jiva, ishwar, maya, etc., are false,' is only meant for one who has attained the nirvikalp state. One who has not realised this state, who performs all worldly activities, believes them to be real and yet negates vidhi and nishedh, is a nastik.
Maharaj further clarifies," ...it was because of the apprehension that such a nastik nature may creep into people's hearts that Shankaracharya composed Bhaj Govindam and many other verses praising Vishnu. He also composed verses extolling Shivji, Ganapati, Surya and many other deities. After hearing these verses, all deities appear to be satya.
"Vedantis also claim, 'Everything is pervaded by Brahma.' However just as the gopis developed affection for Shri Krishna, similarly, all women develop affection for their husbands and men for their wives. Yet they do not attain what the gopis attained; instead, they attain dismal narak (hell). Therefore, the prescribed moral do's and don'ts are indeed true, not false. Whosoever falsifies them will be consigned to narak."