"Advaita" refers to the identity of the Self (Atma) and the Whole (Brahma).
This philosophy was started by Sri Adi Sankaracharya.
Many scholors differ on this and their belief is that this philosophy existed much before Adi sankara and it is mentioned in Uppanishats and Adi Sankara only prophessed it.
Those days Shaivaites and Viashnavaites used to fight and he impressed on people Shiva and Vishnu are same. For common man this is advaitha.
Your vote on this answer has already been received
Advaita Siddhanta (Sanskrit: "non-dual perfect conclusions") Saivite philosophy codified in the agama which has at its core the advaita (non-dual) identity of God, soul and world. This monistic-theistic philosophy, unlike the Shankara, or Smarta view, holds that maya (the principle of manifestation) is not an obstacle to God Realization, but God's own power and presence guiding the Self's evolution to perfection. While Advaita Vedanta stresses Upanishadic philosophy, Advaita Siddhanta adds to this a strong emphasis on internal and external worship, yoga sadhanas and tapas. Advaita Siddhanta is a term used in South India to distinguish Tirumular's school from the pluralistic Siddhanta of Meykandar and Aghorasiva. This unified Vedic-Agamic doctrine is also known as Shuddha Saiva Siddhanta. It is the philosophy of this contemporary Hindu catechism.