In Brihadaaranyak Upanishad, Aatmaa (Soul) is indicated negatively as "Neti, Neti" (not this, not this). The idea behind this is that Aatmaa can not be described as this or that. It is not like a thing or object known to us. This technique is called the "Neti Neti Vaadam" or negative argument. By grammatical rule of conjunction in Sanskrit, na+iti (not this) becomes Neti, which means that which can not be described.

The Kathopanishad says, "a person who is devoid of right understanding, with the mind not held and is always impure (Sadaa Ashuchih) never attains the goal but goes into the round of worldliness (Sansrati) and one who is possessed of right understanding with the mind held and ever pure (Sadaa Shuchih) reaches the goal from where there is no birth again (Yasmat Bhooyo na jaayate). That state is what is referred to as Liberation or Moksh. Purity of mind (Sattwa Sanshuddhih) is said to be one of the characteristics of men of Saattwik disposition who are endowed with Divine Properties (Daivee Sampatti) as stated by Krishn in the Bhagvad Geetaa.

Lord Krishn declares that purity of mind is one of the marks of one who is born with Divine gifts. The inner sense or mind is called Sattwa. Sattwa Sanshuddhih calls for complete elimination of all morbid feelings, such as partiality and prejudice, delight and grief, the feelings of I and mine, infatuation and jealousy etc, as well as impure and sinful impulses of all kinds, from the mind. Purity of mind is the measure of mind's release from the thralldom of the sense organs. The mind thus released is the most wonderful instrument that man should have.

A-Dwaitvaad in Upanishad

Out of the 108 Upanishad, though many of them evince A-Dwaitvaad, Non-Duality Philosophy, four of them have given very open verses related to it. They are ---

"Pragyaanam Brahm" - Brahm is the supreme knowledge - (Knowing the absolute reality is the supreme knowledge)
from Aitareya Upanishad of Rig Ved

"Aham Brahmasmi", meaning "I am Brahm". This Upanishad declares that each one of us are nothing but Brahm (Aatmaa). Who I really am, is that absolute reality.
from Brihadaaranyak Upanishad of the Shukla Yajur Ved

The third Mahaavaakya is the most popular Mahaavaakya, "Tat Twam Asi", meaning "That Thou Art". "That" refers to to the all=pervading Reality, Brahm. "Thou" is the pure Self, which is the core of our personality beyond the five layers of matter (Panch Kosh). This Mahaavaakya pronounces the oneness of the Infinite Brahm and Aatmaa within us. It affirms that the Supreme Reality is nothing but our own Self. That is what you are (That absolute reality is the essence of what you really are).
from the Chhaandogya Upanishad, belonging to the Saam Ved

Incidentally, the Taitteerya Upanishad belonging to the Krishn Yajur Ved contains a slightly different Mahaavaakya "Ahamasmi Brahmasmi" which means "I exist and I exist as Brahm".
from the Taitteerya Upanishad of the Krishn Yajur Ved

The fourth Mahaavaakya is "Ayam Aatm Brahm". It means that "this soul (Aatmaa) is Brahm". Ayam Aatmaa refers to the Self within. The Self or Aatmaa which activates us is the same Brahm which vitalizes the entire Universe. This Mahaavaakya is called an Abhyaas Vaakya which means statement of practice. It is a practical formula given to us to practice and discover the identity between our own Self and the All- pervading Supreme Reality. This Mahavaakya means that the Consciousness in us is nothing other than the Total Consciousness. It is the ultimate declaration for a seeker to realize.
from the Maandookya Upanishad belonging to Atharv Ved

Incidentally, the Mundak Upanishad declares, "Brahmved Brahmaiva Bhavati". It means "The Knower of Brahm becomes Brahm only".
from Mundak Upanishad