O Mother!

Lead me from the unreal to the real

From the darkness to the light

From death(of the ego) to immortality

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Swami says:

Asato maa is the shanti-mantra. The mantra for inner peace. In short it means:

From untruth lead me to to Truth, from darkness lead me to light, from death lead me to immortality.

Even for being blessed by the Lord's Grace, one must have shanti (Inner Peace) and await patiently. Serenity alone succeeds in bringing about the result of Sadhana (spiritual practice). Add this lesson to the practices you are engaged in, night and day, and to the Shanti Mantra.

"Asatho maa sadgamaya;
thamaso maa jyothirgamaya;
mrityor maa amritham gamaya,"

This is the Shanti Mantra. The meaning of this mantra is given variously by various people, some elaborately, some succulently.

" O, Lord, when I am deriving happiness through the objects of this world, make me forget the unreal objects and show me the way to permanent happiness." This is the first prayer.

"O, Lord, when the objects of the World attract me, remove the darkness which hides the all-pervading Atma, which every such object really is." This is the second prayer.

"O. Lord, bless me through Your Grace with Immortality or Paramananda, resulting from the awareness of the Effulgence of the Atma, immanent in every object." This is the third prayer.

This is the real meaning of the Mantra.

It also means:

 From this transient world of decay, lead me to the everlasting world of Bliss;
Give me the effulgence of Thy Grace and illumine my soul with truth; Save me from the torture of birth and death, destroy the cravings of the mind which produce the seeds of birth.

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From: http://archives.amritapuri.org/bharat/mantra/asatoma.php

The first mantra—asato ma sadgamaya—means, "Lead me from the asat to the sat." In fact, it is best to not translate sat (nor its negative counterpart asat) for, as with many Sanskrit words, sat has many meanings and not only are most of them applicable here, their deliberate combined import provides a depth that no one of them could hold independently. These co-applicable meanings include: existence, reality and truth. (Co-applicable meanings for asat being: non-existence, non-reality and untruth.)

We often speak of religion or philosophy as a search for Truth. But only in India's philosophy of Advaita Vedanta has the concept of "truth" been so meticulously and successfully dissected. According to Advaita, for something to be considered true in the ultimate sense, it must be true not just at one given moment, but always be true—true in all three periods of time: the past, present and future. In fact, Advaita goes one step further. It says if something does not exist in all three periods of time that it does not truly exist, it is not ultimately real. Thus, truth, existence and reality are one and the same. That reality, Vedanta says, is what we call God.

The universe and its things are in a constant state of change. The planets are in constant motion, their positions in relation to each other and the other astral bodies are in continuous flux. The seasons similarly are ever-shifting. Scientifically, we can easily understand that our bodies (and the cells within them) come into existence, are born and then go through periods of growth, sustenance, deterioration and death. In fact these six modifications are part-and-parcel of everything in creation. On the level of emotions, we move back and forth between happiness, sorrow and anger. Even our intellectual convictions rarely stay fixed for very long. So, according to Vedanta, we cannot call this world ultimately real. It is not ultimately true. Ultimately, it does not exist. It seems real etc. but it is not. Such a thing is called asat.

The second mantra—tamaso ma jyotirgamaya—means "Lead me from darkness to light." When the Vedas refer to darkness and light, they mean ignorance and knowledge, respectfully. This is so because ignorance, like darkness, obscures true understanding. And in the same way that the only remedy for darkness is light, the only remedy for ignorance is knowledge. The knowledge spoken of here is again the knowledge of one's true nature.

Currently, in the darkness of our ignorance, we believe ourselves to be bound and limited (otherwise we would not be reciting these mantras in the first place). But the Guru and the scriptures are telling us that, in truth, we are not, never will be and never have been bound. Eternally we sat-cit-ananda. The only thing that can remove our ignorance regarding our true nature is a spiritual education at the hands of a True Master like Amma. At the culmination of such an education, light floods the room, as it were; darkness vanishes.

The final mantra—mrtyorma amrtam gamaya—means: "Lead me from death to immortality." This should not be taken as a prayer to live endless years in heaven or on earth. It is a prayer to the Guru for assistance in realizing the truth that "I was never born, nor can ever die, as I am not the body, mind and intellect, but the eternal, blissful consciousness that serves as the substratum of all creation."

It is important to remember that, with all these mantras, the leading is not a physical leading. The Atma is not something far away that we have to make a pilgrimage to, nor is it something we need to transform ourselves into. Atma means "self." We don't need to transform our self into our self. Nor do we need to travel to it. We are it. The journey is a journey of knowledge. It is journey from what we misunderstand to be our self to what truly is our self. What the mantras really means is "Lead me to the understanding that I am not the limited body, mind and intellect, but am, was and always will be that eternal, absolute, blissful consciousness that serves as their substratum."