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Para Brahman (IAST para-brahmaṇ) or Param Brahman (the Highest Brahman; not to be confused with brahmin, an Indic social class designation) is a term often used by Vedantic philosophers as to the "attainment of the ultimate goal". Adi Shankara has said that there is only one Supreme Para-Brahman and all the other deities are the forms and expansions of this Para-Brahman. It is believed that all Vaishnava and other schools attribute Personhood to this concept, as in Svayam bhagavan. Under terms of some schools of Vedanta, It has three modal aspects with a highest as Para Brahman or Lord Vishnu. This term is often quoted often used in relation to Vishnu or Shiva as the ultimate goal of Vedanta. Even Shankara in his commentaries on Yoga Sutras stated, "Through AUM the Lord is met face to face", and "AUM is the Name of the Supreme Lord"(Sabda). One of the most prominent of recent Hindu philosophers, Dr. Radhakrishnan, after his alleged conversion to Gaudiya Vaishnavism in early 1960s, confirmed that this term meant Supreme God as a Person, the Absolute Truth.
ParaBrahman (Sanskrit) [from para beyond + Brahman (neuter) universal self or spirit] - That which is beyond Brahman. The self-enduring, eternal, self-sufficient cause of all causes, the essence of everything in the cosmos. In the Vedic style of writing, ParaBrahman is referred to as tat (that) as opposed to the manifest universe called idam (this). ParaBrahman means Supreme Brahman, or Supreme Cosmic Spirit, or Godhead. Although an ineffable entity, it could be said to be that which contains and pervades the universe. ParaBrahman, from beyond, encompasses the transcendent and immanent ultimate reality, Brahman. The Absolute Truth is both subject and object, so there is no qualitative difference. Terms like Parameshvara, Ishvara, Bhagavan, Brahman, Paramatma are held to be synonymous with ParaBrahman. Shaktas consider Adi parashakti considered as power of ParaBrahman. Hence considered to same. So actually Adi parashakti who does anything (creates, preserve or destroy) on behalf of ParaBrahman because ParaBrahman is static and Adi Parashakti is dynamic essence.
vadanti tat tattva-vidas tattvam, yaj jnanam advayam brahmeti paramatmeti, bhagavan iti sabdyate
brahma-vid apnoti param, tad eshabhyukta, satyam jnanam anantam brahma
Whoever realizes the Supreme Brahman attains to supreme felicity. That Supreme Brahman is Eternal Truth (satyam), Omniscient (jnanam), Infinite (anantam). (Taittiriya Upanishad 2.1.1)
Upanishads further mention often that the Supreme Brahman is Eternal, Conscious, and Blissful (sat-chit-ânanda). 
raso vai sa, rasam hy evayam labdhvanandi bhavati
The One is Bliss. Whoever perceives the Blissful One, the reservoir of pleasure, becomes blissful forever. (Taittiriya Upanishad 2.7.1-2)
Verily know the Supreme One to be Bliss. (Brihadaranyaka Upanishad 2.9.28)
Param Brahman as OM and Parashakti as OM Shakti: Om is the Supreme Brahman. (Svetasvatara Upanishad 1:7) Adi parashakti is considered as the power of Param Brahman. They both are same, whether Vaishnavas or Shaivas, they both consider Her as power of formless and static Param Brahman, Om. What if there is no parashakti, then there will be no GOD. She is cause of all change. The Goddess who is known as the ultimate reality is the adi-parashakti, Goddess Bhuveneshwari . In Shaktism, She is, was and will be only owner and source of this universe and all other universes and is regarded as dynamic form of ultimate reality, Param-Brahman. Shaktas consider her dynamic Param Brahman and Param Brahman is considered as Static Adi parashakti.  When there is no universe, they both unites from which universe is created and when Universe is created, Adi parashakti manifests herself as dynamic in feminine form like Goddess Parvati, Goddess Durga, Goddess Lakshmi and Goddess Saraswati. She is tridevi - the eternal beloved consort of trimurti (Godhead - the three aspects of God)
"The Primordial Power and the Supreme Brahman are identical. You can never think of the one without the other. They are like the gem and its brilliance. One cannot think of the brilliance without the gem, or of the gem without its brilliance. Again, it is like snake and its wriggling motion. One cannot think of the wriggling motion without the snake, or of the snake without its wriggling motion. These are two aspects of Reality: Purusha and Prakriti. He who is the Purusha is also Prakriti. Both are the embodiment of Bliss." -- Sri Aurobindo
nityo nityanam chetanas chetananam eko bahunam yo vidadhati kaman
ete camsa-kalah pumsah krishnas tu bhagavan svayam indras vyakulam lokam mrdayanti yuge yuge
All incarnations are either plenary portions or expansions of plenary portions appearing in various universes to protect the theists; but Lord Krishna is the original supreme lord and the source of all. (Bhagavata Purana 1.3.27-28) 
isvara paramah krishna sac-cid-ananda vigrahah anadir adir govindah sarva karana karanam
Lord Krishna is the supreme absolute controller, whose form comprises immortality, omniscience, and bliss. He is without beginning, the origin of all, the cause of all causes and the source of the Vedas. (Brahma Samhita 5.1) 
namo brahmanya-devaya go-brahmana-hitaya ca jagad dhitaya krsnaya govindaya namo namah
Let me offer my humble obeisance unto Lord Vishnu, who is the worshipable deity for all brahminical people, who is the well-wisher of the cows and brahmanas and who is always benedicting all the universes. (Vishnu Purana 1.19.65) 
Krishna Himself confirms this in the Bhagavad-Gita:
mattah parataram nanyat kincid asti dhananjaya mayi sarvam idam protam sutre mani-gana iva
arjuna uvaca, param brahma param dhama pavitram paramam bhavan purusham sasvatam divyam adi-devam ajam vibhum
Arjuna said: You are the Supreme Brahman, the ultimate abode, the purest, the Absolute Truth. You are the eternal, transcendental, original Person, the unborn, the greatest. (Bhagavad Gita 10.12) 
bhajagovindam bhajagovindam govindam bhajamuudhamate naamasmaranaadanyamupaayam nahi pashyaamo bhavatarane
Worship Govinda, worship Govinda, worship Govinda, Oh fool! Other than chanting the Lord's names, there is no other way to cross the life's ocean. (Bhaja Govindam, composed by Adi Shankaracharya) 
naaraayana paro jyotir-aatmaa naarayana para, naarayanam param brahma tatvam naarayanam para, naarayana paro dhyaata dhyaanam naaraayana para
Narayana is, Para Jyoti, the greatest light, Para Atma, the super soul (Paramatman), Para Tatvam, the best of essences, Para Dhyata, the greatest meditator, Para Dhyanam, the best of meditations. (Narayana Sukta verse 4)
yasya prabha prabhavato jagad-anda-koti-kotishv asesha-vasudhadi vibhuti-bhinnam tad brahma nishkalam anantam asesha-bhutamgovindam adi-purusham tam aham bhajami
Govinda, is the primeval Lord, whose effulgence is the source of the nondifferentiated Brahman mentioned in the Upanishads, being differentiated from the infinity of glories of the mundane universe appears as the indivisible, infinite, limitless, truth. (Brahma Samhita 5.40)
Shiva and Shakti philosophy
Shiva, who is Parameshwara (The Transcendent Lord), who is Satchitananda, issued Shakti. Shakti is not coexistent with Parameshwara but is that Power of Him that is necessary for creation. Shiva and His Shakti are more than the creation which He/She manifests. Shakti, who is the first desire (Kama) of Shiva, is Herself the Divine Mother of the cosmos. When the diverse cosmos emerged from Shiva’s Shakti, the original desire that is the Primordial Will to be pervaded all manifestation. Microcosmically and macrocosmically, as above so below, all is Shiva/Shakti.
We can therefore say that the cosmos is the eternal undiluted Supreme Self expressed expansively from the central core that is Shiva/Shakti, thus enabling the Supreme Self to know, see, and live the Supreme Consciousness through its own self-willed limitation. By so doing the Divine Mother brings forth the stream of Truth embedded consciousness, later expressed as divine law, which is capable of recognizing Her as its primordial source. The cosmos, through this knowing of its source, unites with its Mother in the process of fulfilling the Great Work - Dharma. The penultimate purpose of the cosmos is mergence of the created drop with the ocean that is its Mother. This union is freely achieved within the constraints of Divine Law, brought forth by self limitation of the limitless light that Shiva/Shakti is. The pulsing throb that propels this eternal drive, this thrust for union, is AdiShakti, the Divine Mother as nature. She assumes this mantle without individuality, for She is the equal only of Herself as the silent witness within Her core, and She labours incessantly, through all of Her finite rays of light that define the cosmos, in conscious activity so that they, Her children, may become aware of themselves and merge in the ocean of self realized bliss.
All that is within all universes pre-exists within the Mother, for nothing can manifest that is not previously existent within Her womb. All evolution being directed towards perfection is the direct result of an innate knowing, a blueprint of limitless possibilities, brought forth by that which is resident within Shiva. This Principle precedes the expression, for without the Principle there can be no expression of its Will. Something does not emanate out of nothing.
Hindu sects like Shaivism, Vaishnavism and Shaktism have concept of ParaBrahman. However, in contrast with Vaishnavism where ParaBrahman denotes Saguna Brahman as Hari or Vishnu, either Saguna Brahman or the impersonal Nirguna Brahman may be connected by other sects. It is also customary that followers of a particular sect view other personal forms of God as expansions or aspects of the Supreme Being.
References and notes
- Sawai, Y. (1987). "The Nature of Faith in the Sankaran Vedanta Tradition". Numen 34 (1): 18–44. doi:10.1163/156852787X00128. JSTOR 3270048.
- Malkovsky, B. (1997). "The Personhood of Samkara's" Para Brahman"". The Journal of Religion 77 (4): 541. doi:10.1086/490065. JSTOR 1206747.
- White, C.S.J. (1970). "Krsna as Divine Child". History of Religions 10 (2): 156. doi:10.1086/462625. JSTOR 1061907.
- His Thought, I.S. (1992). "Radhakrishnan: His Philosophical Position". Tagore and Radhakrishnan, a Study in Religious Perspective.
- Om in the Upanishads
- [www.adishakti.org Adi Shakti global website]
- Bhagavad-gītā as it is By A. C. Bhaktivedanta Swami Prabhupāda, pg. 334-335
- Parabrahma: Bhakti Yoga Dictionary on Parabrahma
- Krishna, The Supreme Personality of Godhead
- Para-Brahma Upanishad
- Para Brahma Upanishad
- "VEDA - Vedas and Vedic Knowledge Online - Vedic Encyclopedia". www.veda.harekrsna.cz.