Of the nature of Sat (Existence), Chit (Consciousness) and Ananda (Bliss), Brahman is the absolute non-dual reality. There is nothing apart from Brahman here. Whatever exists is only an illusion of names and forms in Brahman. Thus we all are Brahman only.
That which doesn't ultimately exist but seems to exist empirically. That which is beyond logic and intellect. The cause of names and forms (or creation in short). Illusory power of Ishwara (who is Brahman associated with this power).
Superimposition of the reality on the unreality and vice-versa. Eg: snake being superimposed on the rope. In Vedanta, adhyaasa is superimposition of the Self on the not-Self (considering the not-Self of body-mind-intellect to be real) and of the not-Self on the Self (considering the not-Self of body-mind-intellect to be "I"). Adhyaasa is the cause of all our sorrows and sufferings in the world - in Sankara's words, adhyaasa is anartha hetu (cause of anartha or miseries). Sankara's introductory commentary to the Brahma Sutras where he explains the need and necessity of learning Brahma Sutras is titled Adhyaasa bhashya because of the detailed analysis of adhyaasa.
Jeeva is the reflection of Consciousness in the intellect which gets associated and attached to the body-mind-intellect complex. Is equivalent of ahamkaara or Ego. We generally consider ourselves as the jeeva whereas we are the Original Consciousness of Atman which is realized when the jeeva is purified (purification means removal of the intellect which in turn would merge the reflection in the intellect into the original).
Unmanifested state of Brahman associated with Maya prior to getting manifested. Equivalent of the deep sleep state wherein we are merged into the Self in a state of unmanifested existence which then leads to manifestation of dream and waking worlds.
The process of quantuplication wherein each of the fiver primal elements gets split into two halves. Each half again gets split into 4. Each 1/8th gets added/married to other elements. Thus Ether will end up with 1/2 ether, 1/8 air, 1/8 fire, 1/8 water and 1/8 earth. Similarly with Air, Fire, Water and Earth.
Doubting faculty of the antah karana which enters into sankalpa and vikalpa (doubts and imaginations). When a person is coming towards Rama, Rama thinks "Is this my friend Krishna?" - this is mind functioning.
Five sense organs of perception which include ears (sound), skin (touch), eyes (sight), tongue (taste) and nose (smell). The physical parts that we see aren't the indriyas but just the openings through which the indriyas function. This is clearly known through a person having physical eyes but still not able to see things.
Though Prana or vital force that sustains life is one alone, it is split into five based on the functionality and the parts of the body where it functions. Pancha pranas are prana, apana, vyana, samana and udana.
Also known as linga shareera, this is composed of 17 parts of pancha jnaana indriyas, pancha karma indriyas, pancha pranas, manas and buddhi (some places it is considered as having 18 or 19 parts depending on the addition of chitta and ahamkaara).
Dreamless deep sleep where we don't perceive either gross world or subtle world. This is a state having just two experiences as pronounced by us when we wake up from the state - "I slept happily" (happiness) and "I didn't know anything" (ignorance). This state is very similar to the state of liberation - difference being in ignorance resulting in unawareness of the happiness in the deep sleep state.
Literally meaning that which has been heard or that which has been revealed. The Vedas are the sruthi as they are without any beginning and has been revealed to rishis during times of deep absorption. It is also called sruthi as it is learnt through oral teaching. Rishis are not mantra karthas but mantra dristas or seers of mantras which are the verses of the Vedas.
Literally meaning that which has been remembered or memorized or caused out of the intellect. Smrithi is secondary source of knowledge unlike Sruthi which is the primary source. Smrithi depends on Sruthi for its authority and validity. Anything in Smrithi which contradicts Sruthi is ruled out. The most common smrithis are Bhagavad Gita, Manu Smrithi and Yajnavalkya Smrithi.
Word by word detailed commentary on a particular work. Bhashya cannot go against the work and hence it explains the original work by relating the words in order and explaining each of the words. The most famous bhashyakara is Sankara who has written bhashyas on the prasthaana trayas of Upanishads, Gita and Brahma Sutras.
Vyaakhya is a detailed explanation of a particular work. Unlike bhashya, vyaakhya might or might not explain each of the word in the original work but it does explain in depth the entire sloka of the work. The most famous vyaakhyakara has been Rama Tirtha of 16th century who was the advaita Guru of Madhusudana Saraswathi and who wrote vyaakhyas on Upadesa Sahasri, Vedanta Saara, Sankshepa Sareeraka and Dakshinamurthy astakam among many others.
Tika is a gloss on a particular work. This will not explain in detail the original work nor will it deal the explanation of each word in the original work. It just gives in brief the explanation of the entire sloka. The tikakara in advaita is Ananda Giri who has written tikas on Sankara's prasthaana traya bhashyas.
Vartika speaks about three things -- uktha, anuktha and duruktha of a work. Uktha is whatever has been mentioned in the original work will be explained. Anuktha is explanation of things that has been missed out in the original work. Duruktha is explanation of things that has been wrongly mentioned in the original work. Unlike bhashya and other types of commentaries, Vartika can go against the original work. Vartikakara of Advaita is Sureshwaracharya who has written vartikas on Sankara's Brihadaranyaka and Taittiriya bhashya, Manasollasa on Dakshinamurthy astakam and Panchikarana Vartikam.