Om

Om (sometimes written as Aum) is the universal syllable, the primordial sound, and the universal mantra that contains all other mantras. It is an excellent mantra to chant aloud. To do it properly, the sound should come from as deep within the body as possible, in a totally relaxed state. Your personal Om is the sound that is easiest to make, with your throat totally relaxed, vibrating deep in your body and coming up from the base of your spine. Once you have done it for awhile, it will resonate in rhythm with your heartbeat, and it will help you to slow your heartbeat down.
But
Om is more than a sound. It's the symbol of the
Brahman, the universal Self. When you chant "
Om" you should FEEL the sound and keep it associated in your heart with That which is infinite, eternal, immortal, free, unchanging, the Brahman. You should FEEL that you are That.
Another very simple mantra is "Om Tat Sat." That translates loosely as "all is truth," but the meaning is much more all-encompassing. Because Om takes in everything, to begin with. Because Tat "That" is the inexpressible in words, the absolute reality, the Brahman, that can only be pointed at but not described. And because Tat is not just "Truth" but is also Bliss and Freedom.
In fact most of the really great mantras begin with
Om, as for example, "
Om Namah Shivaya" and the
Gayatri Mantra.
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