Enlightenment is ultimately about clearing up a simple misconception about who you are. The simplicity of it all is illustrated by the classic story of the tenth man.
Ramana Maharshi's self-inquiry and traditional advaita vedanta
Ramana Maharshi's simple self-inquiry instruction -- to attempt to chase and locate the "I" -- may seem, at first glance, to be quite different from the more scriptural and thinking-based instruction of traditional advaita vedanta. But this difference is only on the surface. Both ultimately come to exactly the same method from just slightly different angles: quiet the mind and discern away the unchanging by investigating the "I" thought. By doing so, the normal I disappears and an intuition is generated which destroys ignorance. What is left is the Self, which was always there, but simply was't recognized because of that ignorance.
The concept of satori & advaita vedanta: stillness & insight
Satori is the concept in Japanese buddhism that suggests a profound, sudden insight. It is cultivated out of mental silence and concentration, but is not simply the same as them. Out of stillness, a looking or noticing emerges. The same scheme is present in advaita vedanta. Mental purity and then discernment or looking happens -- and that results in true knowledge. The fruit of knowledge is further silence.
The riddle-like nature of self-inquiry: where is God?
Self-inquiry -- the search for the true "I" -- cannot simply be a matter of any kind of concentration or search by the mind. One can quiet the mind that way, but then one hits a wall. But that mental search quiets the mind and, eventually, through a process of concentration, allows something to emerge that goes beyond the conceptual. I demonstrate through the Hindu story of Prahlada, and with reference to the text Vakya Vritti.
Unbroken concentration is the means and the end of spiritual liberation
All spiritual paths are ultimately aimed at moving away from the rufflings of thought and towards the smooth, unbroken concentration that is initially pursued with effort, but is finally simply recognized as our true nature.
Oriented towards the thought that isn't a thought, thought is cut up, evaporates, and peace remains
Through self-inquiry and surrender, we orient towards the thought that is the base of all other thoughts... the thought that isn't a thought, that is our Self. Its vast impenetrable space is that against which all other thoughts dash themselves and evaporate harmlessly. Orienting towards that, we realize that there is nothing but that orientation, effortlessly and always.
Traditional advaita vedanta vs. neo-advaita
Traditional advaita vedanta (the 'nondual' school of Hindu mysticism) is often contrasted with so-called neo-advaita, but what are the real differences between the two? The key hinges on the meaning of neo-advaita, which has been interpreted in two dramatically different ways. The first way, which simply says no effort is needed or possible, is justly criticized. The second way, which emphasizes inward looking, is actually just a rephrasing of traditional advaita vedanta from a different perspective.
The nature of the nondual Self: even ignorance is knowledge, even suffering is bliss -- effortlessly
The Self is not something that depends on our thinking about it a certain way, or on penetrating some kind of illusion of our own individuality. That IS the very illusion that we are seeking to penetrate. The Self is effortless peace and bliss, whether we like it or not. Even our thoughts of ignorance and suffering are that, whether we know it or not, whether we remember it or not.
The ordinary absorptions ("samadhis") of waking life
I take a look at a short passage from the wonderful scripture Tripura Rahasya (The Secret of the Supreme Goddess) to illustrate how seekers must learn to identify the relative Self -- which is the quiet mind, the absence of distinctions -- before moving on to understand the Self as beyond any such distinctions.
Turn away from what you want or pursue it? Old vs. new school spiritual approaches to desire
The nondual traditions have usually held that the seeker must turn away from desires for fulfillment in the world -- through relationships, pleasure, etc. The seeker should use knowledge and the cut the attachment to these. My approach is a bit different. The seeker must indeed turn away from seeking happiness in these pleasures, but this is only going to happen through a process of honest admission and pursuit of desire. The old knowledge+willpower way doesn't work that well.