Does any one know what this(Shakti Visishtadvaita) philosophy is all about? I know what are dvaita, advaita philosophies but this is new one.
Shakti Vishishtadvaita is the philosophy of a Shaivite sect known as Lingayatism, AKA Virashaivism, founded by the 12th century philosopher Basava. Note that the term "Shaivite" actually means something here; there are a lot of people who call themselves Shaivites, like Iyers for instance, but they're actually followers of Adi Shankaracharya's Smartha sect (which I discuss here and here) and simply adopt Shiva as their personal god. The Lingayatas, on the other hand, are actual Shaivites, in the sense that they really view Shiva as the supreme being, and not just one among a number of equally valid ways to conceptualize Brahman.
In any case, the Shakti Vishishtadvaita philosophy of the Lingayata sect is a variant of the Vishishtadvaita Vedanta philosophy of the Sri Vaishnava sect (of which I'm a member). The fundamental difference between different Vedantic philosophies is the relationship between Jivatatmas (individual souls) and Paramatma (the supreme soul or supersoul). According to Adi Shankaracharya's philosophy of Advaita, Jivatma and Paramatma are one and the same, and according to Madhvacharya's philosophy of Dvaita, Jivatma and Parmatma are completely seperate. The standard version of Vishishtadvaita, or "qualified monism", takes a middle view: it says where there is one big unified whole called Paramatma, but within that there are still distinct parts like Jivatmas, akin to how an unborn baby is part of the body of a pregnant woman, but the pregnant woman's body extends beyond the baby (what Western thinkers would call panentheism).
Shakti Vishishtadvaita, or "monism qualified by Shakti", is a modification of this view, where Shiva is not merely united with seperate beings called Jivatmas, but rather he transforms himself into Jivatmas and the world, so that the Jivatmas and the world exist but are still have "Shiva-ness". This transformation is done through the power of Shakti, Shiva's energy, who is considered non-different from Shiva himself. Here is how this website characterizes the philosophy:
Vimarsha Shakti exists in Shiva by the relation of Samarasya or identity, just as heat and light exist by the relation of identity in the fire and the sun. In other words, between the substance and the attribute there is an inseparable union or essential identity which points to reality that continues to remain in the character of individual organic Whole. It is for this reason that Siddanta Shikhamani speaks of intrinsic and ever abiding in Shiva. Hence he is characterized and distinguished by his self-conscious power to work wonders. This is Shaktivishistadvaita. Here Vishista does not suggest any inseparable union of two or more entities like soul, world and God of the Ramanuya system or of South Indian Shaivism. Vishistattva simply connotes the nature of Vimarsha, namely the self-conscious power of Shiva. Because of this Divine energy or Chit-shakti which has the power of doing, undoing and doing otherwise, Shiva transforms Himself into the world without ceasing Himself to be. Hence, Veerashaivism maintains Shivaparinamavada....
In the case of Sankhya and Ramanuja, it is Prakrti Parinamavada but in Veerashaivism it is Shiva Brahma parinamavada. The world comes out of the very essence of Shiva and not from maya, or body or even power of God as found in the other systems. In upholding the doctrine of the transformation of essence (svarupa parinamavada), Veerashaivism remains most faithful to the Scriptural authority. God happens to be both the material and efficient cause of the world, though God becomes the world by the process of modification. He does not suffer any change within Himself. The world is the Sat-aspect of God and therefore a real manifestation of Him and not an illusion. It is non-different from Him; the relation between the two is that of the identity of cause and effect. The world gives us an idea of the greatness of God, and those who realize this greatness cannot but worship Him. In the words of Hegel, the reality of the world supplies the individual with the religion of majesty in which the reflecting mind is overwhelmed by the contemplation of the manifestation of the Divine Being.
One of the best ways to understand a Vedantic philosophy is through its commentary on the Brahma Sutras, the defining text of the Vedanta school as I discuss here. So for more information about Shakti Vishishtadvaita, you might want to read C. Hayavadana Rao's introduction to the Shrikara Bhashya, the Shakti Vishistadvaita commentary on the Brahma Sutras. Here it is in PDF format. (I downloaded it from the Digital Library of India and then re-uploaded it to Google Drive.)