Adi Sankaracharya, incarnation of Lord Shiva:
Adi Shankara was the first in the tradition to consolidate the siddhanta ("doctrine") of Advaita Vedanta. He made commentaries and Stotras. He traveled length and breadth of India. He won all the debates he undertook. He did every thing in a short span of his life of 32 years!
1) Bhashyas (commentaries);
Adi Shankaracharya was the first to make Bhashyas (commentaries) on ten principle Upanishads, the Bhagavad Gita, Brahma Sutras, Yoga Suthras, Sri Vishnu Sahasranamam and Sri Lalitha Trishathi
2) Hymns and Treatises:
In addition Sri Bagavadhpada wrote the following Sanskrit Granthams:
Sri Ganesha Pancharathnam, Sri Ganesha Bhujangam, Sri BalaMukundastakam, Sri Bhaja Govindam, Sri Manisha Panchakam, Sri Meenakshi Pancha Rathnam, Sri Soundarya Lahari, Sri Sivananda Lahari, Sri Subramanya Bhujangam, Sri Sarada Bhujangam, Sri Shiva Manasa Pooja, Sri Manthra Mathruka Pushpamala Sthava, Sri Rajarajeswari Astakam, Sri Bhaja Govindam, Sri Kanakadhara Sthavam, Sri Ardha Nariswara Stothram, Sri Kala Bhairavastakam, Sri AnnaPoornastakam, Sri Kashi Panchakam, Sri Manikarnika Stothram, Sri Kashi Stothram, Sri Lakshmi Narasimha Karavalampanam, Sri Achyutastakam, Sri Shathasloki, Sri Dashasloki, Sri Gangastakam, Sri Yamunastakam and Sri Narmadastakam
3) Dig-vijaya and debates:
One of the most famous debates of Adi Shankara was with the ritualist Maṇḍana Misra. After debating for over fifteen days, with Manaana Misra's wife Ubhaya Bharati acting as referee, Mandana Misra accepted defeat. Ubhaya Bharati then challenged Adi Shankara to have a debate with her in order to 'complete' the victory. Adi Sankaracharya won that debate also.
He travelled throughout India, from South India to Kashmir and Nepal, preaching to the local populace and debating philosophy with Hindu, Buddhist and other scholars and monks along the way.
With the Malayali King Sudhanva as companion, Shankara passed through Tamil Nadu, Andhra Pradesh and Vidarbha. He then started towards Karnataka where he encountered a band of armed Kapalikas. King Sudhanva, with his Nairs, resisted and defeated the Kapalikas. They safely reached Gokarna where Shankara defeated in debate the Shaiva scholar, Neelakanta.
Proceeding to Saurashtra (the ancient Kambhoja) and having visited the shrines of Girnar, Somnath and Prabhasa and explaining the superiority of Vedanta in all these places, he arrived at Dwarka. Bhatta Bhaskara of Ujjayini, the proponent of Bhedabeda philosophy, was humbled. All the scholars of Ujjayini (also known as Avanti) accepted Adi Shankara's philosophy.
He then defeated the Jainas in philosophical debates at a place called Bahlika. Thereafter, the Acharya established his victory over several philosophers and ascetics in Kamboja (region of North Kashmir), Darada and many regions situated in the desert and crossing mighty peaks, entered Kashmir. Later, he had an encounter with a tantrik, Navagupta at Kamarupa.
4) Accession to Sarvajnapitha:
Statue of Adi Shankara at his Samadhi Mandir, behind Kedarnath Temple, in Kedarnath, IndiaAdi Shankara visited Sarvajnapitha (Sharada Peeth) in Kashmir (now in Azad Kashmir, Pakistan). The Madhaviya Shankaravijayam states this temple had four doors for scholars from the four cardinal directions. The southern door (representing South India) had never been opened, indicating that no scholar from South India had entered the Sarvajna Pitha. Adi Shankara opened the southern door by defeating in debate all the scholars there in all the various scholastic disciplines such as Mimamsa, Vedanta and other branches of Hindu philosophy; he ascended the throne of Transcendent wisdom of that temple
5) Establishing Mutts:
Adi Shankara founded four Mutts (Sanskrit: मठ) to guide the Hindu religion. These are at Sringeri in Karnataka in the south, Dwaraka in Gujarat in the west, Puri in Orissa in the east, and Jyotirmath (Joshimath) in Uttarakhand in the north. Hindu tradition states that he put in charge of these mathas his four main disciples: Suresvara, Hastamalakacharya, Padmapada, and Totakacharya respectively.
6) Shanmatha Sthapaka:
Sri Sankaracharya, combined all the 72 religious sects, which were prevailing in his time to just six, which are as Ganapathyam, Koumaram, Shaktham, Shaivam, Vaishnavam and Souram.
7) Adi Shankara Sthuthi;
श्रुतिस्मृतिपुराणानामालयं करुणालयम्|
नमामि भगवत्पादशंकरं लोकशङ्करम् ||
sruti smrti purananamalayam karunalayam|
Namami Bhagavatpadasankaram lokasankaram||
I salute the compassionate abode of the Vedas, Smritis and Puranas known as Shankara Bhagavatpada, who makes the world auspicious.