What are some of the principle methods of concentration?

Response by Learner MD

The method of concentrated meditation:
The human mind is mostly fickle and unstable and comprehends only by division and separation. Therefore first it is important to train the mind to be focused on one single idea or thought that is the object of our concentration. Nothing should be allowed to distract the mind from its object of concentration. Once this is achieved then the tapas of the mind enables it to break the barriers of its own confines and with the help of the will of the soul, reach the essence or consciousness of the thing that it was seeking, allowing a full manifestation of the object of knowledge. And then either slowly or rapidly the exclusive concentration of the mind turns to an integral experience and realization of the whole being and all its parts. Finally the thing achieved must be held and dwelled upon till it becomes a natural, self existent substance of the being.

The method of inner contemplation:
Another method is that of an inner ascetic contemplative concentration or inner Samadhi. Here the object is sought in its essence and not in its entirety of experience. Here thought slowly ceases and passes into an inner exclusive meditation where the being unites with the seed of the object in an upward or inward movement. The object is achieved here too but only in an elevated condition and an unbridgeable gulf is felt as soon as the inner state is lost or the awakened state is brought back. “This truncated possession is not the aim of an Integral Yoga.”

The method of inner silence:
In this method the aim is to bring the mind to a silence first. This is done either by watching all thought as a witness without participating in its frivolous activity and then allowing all activity to cease out of sheer “unsanctioned leaping” or by rejecting fiercely all thought and clinging to the silence that exists behind the mind and its noise. When that inner peace is unveiled then it is possible to reach to the supreme silence of the Brahman. And this in turn forms the basis of all true knowledge, and thence anything can be known and realized.

Comment by LS to MD

MD, your answers are correct and very clearly expressed. Regarding techniques of meditation, I don't think you have discussed the method of allowing the mind to dwell upon a particular idea in thought. This is not concentration per se, but the thoughts are kept focused on the subject of the meditation. Also, there is another method of bringing silence into the mind, though I don't think it is mentioned here in the text, and that is by calling it down into one. In fact I believe this is the easiest way.

“Purity and concentration are indeed two aspects, feminine and masculine, passive and active, of the same status of being; purity is the condition in which concentration becomes entire, rightly effective, omnipotent; by concentration purity does its works and without it would only lead to a state of peaceful quiescence and eternal repose.”
Sri Aurobindo, The Synthesis of Yoga
CWSA, vol 23-24, p. 317