Advaita means „one without second“
If any one attempts to study or understand Sankara and the concept of Advaita, it is advisable to note the following tips:
Do not start comparing or contrasting with other systems of Philosophy or their protagonists, alongside. Just what Sankara conveyed should be the focus. Ask as many questions as you wish, in order to accept or reject his vision, totally or in parts. Be convinced before you accept any. Do not try to say he is better or worse than another similar Acharya. Evaluate Him on the basis of the logic, the science and our own understanding of what he says. Challenge Him, where and when necessary, he likes it and brings you round. He never professes blind faith in anything.
ADVAITA means ONE WITHOUT SECOND. There is only Brahman, and nothing else. Just nothing else. Therefore, everything conceived, seen, experienced etc. is Brahman. I am Brahman, you, he, she, the animals, the birds,the reptiles, the inanimate matter and the products, the elements, you name it, IT IS BRAHMAN. In this sense, the thief, the robber, the murderer, the cheat are all Brahman, just as the seers, the kings, the good people all are. Read Anuvaka 3 of Sri Rudram - a part of and central piece of Yajurveda -catalogues these negatives and confirms that these are all Sri Rudra!
At first sight, this sounds outrageous, but then Sankara says that the Universe that is perceived is unreal. It is the product of Maya. It appears to be real, but is not. It is 'mind stuff'. The sky, the rainbow etc. are all seen but they are only reactionary, depending for existence on something else. The rising and setting of the Sun are unreal, there is neither. Why then do we allow ourselves to be deluded? Because of Avidya that clouds our Mind . Like a bath room mirror that is misty and cannot reflect an image, it is unable to perceive the truth behind these appearances. Once the mist mirror is cleaned dry or the Mind is cleaned free of all pulsations the truth of the Unity i.e. Brahman arises. The created Universe, all else cease to exist. In fact, these never existed except in our imagination.
How does one clean the Mind. By right (Satwic) thoughts, speech and action, accompanied by total detachment but holistic involvement. These produce no results that bind you. On the contrary, if one is attached to the activities or their results, he gets involved with the Universe that is 'non est'. This will involve him in the cycle of continuous births and deaths and all the good and bad experiences of existence. The Bhagavad Gita is Krishna'a manual for life and for realisation of Reality.
Ramanuja and Madhwacharya came later, historically, and varied the Sankara doctrine in line with their own convictions and needs of the time.