Sri Adi Sankaracharya the world's greatest Guru (Jagathguru) is considered an incarnation of Lord Shiva. He purified Vedic knowledge by teaching discernment and he instituted the worship of deities as worshipping different forms of the one God.
When the people were not living in accord with their inherent spirituality, all the gods and rishis went to Kailash and pleaded with Lord Shiva to revive the world. Lord Shiva agreed to their request and informed them that he would be born into this world.
There was a Nambudri Brahmin couple, Shivaguru and Aryamba, in a little village, called Kaladi, situated on the banks of River Poorna (Purana / Periyar), in the state of Kerala. The couple had remained childless for a long time. They went to Thrissur (Trichur) and performed puja for several days to Lord Vadakkunnathan (Lord Shiva) and prayed for a son.
Lord Shiva appeared to the couple in their dream and promised them a choice of one son who would be short-lived, but the most brilliant philosopher of his day or number of ordinary children who will live long. The couple replied the decision could not be theirs as the Lord knows what is good for them and thereby Shankara was born.
His father died while Shankara was very young, and his mother performed his Upanayana (sacred thread ceremony) with the help of her relatives and he was sent to Gurukul (Vedapatasala) for learning of scriptures. As Shankara grew up, he excelled in all branches of traditional vedic learning and attracted everybody with his intelligence and kindness.
As per the practice the Brahmachari has to go from house to house and take alms and submit this to his guru. One day, Shankara happened to go to the house of a very poor lady and asked for the alms. The lady did not have a single grain of rice in her house to give, but did not want to send away the boy (Shankara) empty-handed, gave him the Amla fruit which was the only thing available in her house. Sensing the abject poverty and selflessness nature of the lady, Shankara composed a beautiful stotra called "Kanaka Dhara Stotra" and prayed to Goddess Lakshmi to extend Her Grace on the poor lady. On completion of this stotra, Goddess Lakshmi appeared in person and showered a rain of golden coins on the poor lady's house.
Sankara returned home from Gurukula after mastering the Vedas and many other subjects. At home, he spent his time in studying the Vedas, serving his mother and performing the ordained rituals.
One day, the rishis came to him and reminded him of his duty to the land in spreading spiritualism. Shankara agreed to become a Sanyasi and go all over the country to spread spiritualism. But Shankara's mother wanted her son to be her support at old age and did not want to become a Sannyasi.
One day, when Shankara was bathing in the river, a crocodile caught hold of his leg. Shankara called out to his mother. Aryamba came running and to her horror she found her son in the grip of the crocodile and she cried that she did not know how to help her son. Shankara informed his mother that his life was nearing to an end, but if he became a Sannyasi, he could start a new life as a sanyasi. The reluctant mother agreed. Thus Sri Sankara obtained permission from his mother to become a sannyasi. Shankara at that time composed the famous stotra called "Sri Lakshmi Narasimha Karavalamba Stotra".
To comfort his anxious mother, he promised that he would return at the moment of her death, to conduct her funeral rites, notwithstanding the fact that he would be a sanyasi then. He prayed to Lord Krishna (this is the famous Sri Krishna Sri Krishna Ashtakam) in the temple near Poorna river, to be a eternal support for his mother. This famous temple of Krishna is there even today in Kaladi.
Shankara then left Kerala and travelled through the present Karanataka towards North India in search of a Guru. On the banks of the Narmada River (near Omkareswarar Temple, a Jyotirlinga of Lord Shiva), he met Govinda Bhagavatpada. When Govinda Bhagavatpada asked Shankara's identity, he replied with an extempore verse that brought out the Advaita Vedanta philosophy (Nirvana Shatkam). Govinda Bhagavatapada was impressed and took Shankara as his disciple. Sri Govinda Bhagavatapada taught various vedas to Shankara. He also taught about Advaita, the principle that everyone in this world is the manifestation of God and that God and Atman are one and the same. Then Govinda Bhagavatpada instructed Shankara to write a Bhashya (commentary) on the Brahma Sutra and spread the truth (Advaita philosophy) far and wide.
Shankara travelled to Kashi (Varanasi) where he spent some more to write commentaries on major Upanishads and Gita. A young man named Sanandana (Padmapada), hailing from Chola territory in South India, became his first disciple. While on his way to the Vishwanath Temple, a Chandala accompanied by four dogs came in the way of Sankara. When asked to move aside by Shankara's disciples, the untouchable replied: "Do you wish that I move my everlasting Aatman ("the Self"), or this body made of flesh?" Realizing that the Chandala was none other than god Shiva himself, and his dogs the four Vedas, Shankara prostrated himself before him, composing five shlokas known as Manisha Panchaka.
Sankara came to know intuitively that his mother was dying, and decided to visit her. He spent a few days with his mother and after she had died. Remembering his promise to her, he performed her funeral rites. His orthodox relatives would not permit him to do the rites himself, as he was a sanyasi, but Sankara overrode their objections, and built a pyre himself and cremated his mother in her own backyard. After this, he once again resumed his travels and the noble mission.
One day, Shankara went to a Vedapatasala in Varanasi (Kashi). He was pleased to see young boys chanting Vedas. An aged scholar was teaching the rules of Sanskrit grammar to his students by rote. Taking pity on him, Adi Shankara went up to the scholar and advised him not to waste his time on grammar but to turn his mind to God in worship and adoration. Then Shankara immediately composed the famous "Bhaja Govindam" which is the highest truths of Vedanta. It is also called Moha Mudgara.
Shankara went to Badrinath. Lord Vishnu appeared before him and told that his sculpture in Alaknanda river should be taken out and a temple should be built for it. Shankara discovered a Saligram stone image of Lord Badrinarayan / Badrinath (Vishnu) in the river. This temple is called Badrinarayan temple (one of the 108 Divya Desams) which is one of the holiest for Hindus. Similar to Badrinath, Sri Adi Shankara is said to have worshipped in Kedarnath temple (one of the 12 Jyotirlingas of Lord Shiva built by the Pandavas) and formulated the worship protocols. It is also believed that Adi Sankara attained Samadhi near Kedarnath temple. The Samadhi of Adi Shankaracharya is located just behind the Kedarnath temple.
Shankara established five Mathas / Peettahs one at Sringeri in the south at Karnataka for the propagation of Yajur Veda, the second on the East at Puri in Orissa for Rig Veda, third at Dwaraka for Sama Veda in the West at Gujarat and the fourth at Badari in North in Uttar Pradesh for Atharvana Veda. According to some accounts, he set up a fifth Matha at Kanchipuram. He established Dasanami, or ten orders of Sanyasis attached to these Mathas. These five pittahs are effectively functioning even today as per the priciples and procedures laid down by Sri Adi Sankaracarya.
Shankara travelled across the Indian subcontinent (Digvijaya Yatra) to propagate his philosophy through discourses and debates with other thinkers.
In Shankara's time, there were innumerable sects following their own narrow philosophies and systems of worship. People were totally blind to the underlying common basis of the One God. For their benefit, Shankaracharya formulated the Shanmata system of worship which brought to the fore the main godheads - Vaishnavam, Shaivam, Shaaktam, Gaanapatyam, Kaumaaram, Sauram - Vishnu, Shiva, Shakti, Ganesha, Skanda and Surya. He also formulated the rituals and rites to be followed in most of the major temples in India, which is even followed today.
The existence of Vedic Dharma in India today is due to Shankara. The forces opposed to Vedic religion were more numerous and powerful at the time of Shankara than they are today. Still, single-handed, within a very short time, Sankara overpowered them all and restored the Vedic Dharma and Advaita Vedanta philosophy. The weapon he used was pure knowledge and spirituality.