Can someone please tell me about the principal teachings and methodology of Jiddu Krishnamurti and his approach towards spiritual progress ? Some people also believe that he was also related to "Maitreya".
Jiddu Krishnamurti an Iyer Brahmin although didn't identify himself with any sect or creed, his teachings are extremely valuable to the followers of Hinduism especially for Advait Vedantists, and Kashmiri Shaivas as he lays ground for their followers to practice Self-related teachings more ardently and also because his teachings are not at all in contradiction with Advait sects. How? Because like Advaita sects aim at transforming one's ontology, JK aims at transforming psyche. And of course, working on ontology without working on psychology breeds hypocrism and theorecity. This was the reason why Adi Shankara was also reluctant to allow Non-Dvijas to read Vedanta (Non Dvijas need to work on their psyche first). So, JK teachings aims at transforming psyche. His whole teachings revolve around conditioning and how to free from them. His principle teachings are
Observer is observed: it means the psycho-physical 'I' which is conditioned with fear, attachments, sorrows etc is no different from these qualities together. In other words, these qualities are what has created fake 'I'. Now this is not only a theoretical concept. But it is actually worth applying in practice.
Choiceless awareness: it is to observe the things and event without any acceptance or rejection towards the objects to be observed. That too, without observer after understanding 'observer is observed'. In simple words, it is 'being's rather than 'becoming' which is ShAmbhavopAye in Kashmiri Shaivism.
As far as his relationship with Maitreya was concerned, Theosophical society had accepted and about to declare he was finally possessed by Maitreya ( probably future Buddha), he stepped back from all his association with the society declaring this
I maintain that Truth is a pathless land, and you cannot approach it by any path whatsoever, by any religion, by any sect. That is my point of view, and I adhere to that absolutely and unconditionally. Truth, being limitless, unconditioned, unapproachable by any path whatsoever, cannot be organized; nor should any organization be formed to lead or to coerce people along any particular path. If you first understand that, then you will see how impossible it is to organize a belief. A belief is purely an individual matter, and you cannot and must not organize it. If you do, it becomes dead, crystallized; it becomes a creed, a sect, a religion, to be imposed on others. This is what everyone throughout the world is attempting to do. Truth is narrowed down and made a plaything for those who are weak, for those who are only momentarily discontented. Truth cannot be brought down, rather the individual must make the effort to ascend to it. You cannot bring the mountain-top to the valley. If you would attain to the mountain-top you must pass through the valley, climb the steeps, unafraid of the dangerous precipices. ( Read complete lecture here)
As far as his teachings are concerned and whether he actually was possessed by future Buddha or not. But he indeed sounds like Buddha.
Below are the links to read his workings, but it is recommended to read his first book - Freedom from known (which is the first book he wrote after enlightenment).
I finally would like to end with these lines taken from here -
Lo! the hour has come,
The hour that I have known.
Liberated am I,
Free from life and death.
Sorrow and pleasure call me no more,
Detached am I in affection,
Beyond the dreams of the Gods am I.
As the moon is full and serene
In the days of harvest,
So am I
In the days of my Liberation.
Simple as the tender leaf am I,
For in me are many winters and many springs.
As the dewdrop is of the sea,
So am I born
In the ocean of Liberation.
As the mysterious river
Enters the open seas,
So have I entered
Into the world of Liberation.
This is the end I have known.