What Advaita Vedanta says about purpose
Advaita Vedanta answers this question by taking it apart. Ask what to do with your life and the tradition asks who is asking, then says the thing being looked for is not in front of you. That makes it unusual reading on purpose, because the work it prescribes is preparation and the goal is not an achievement. Nine concepts below, some from Shankara's school and some from the twentieth-century teachers the library includes.
Mumukshutva — Burning Desire for Liberation
Advaita counts the wish for freedom as a qualification rather than a reward. Wanting it is already the beginning of it, on this account.
Vivekachudamani 27
Nitya Anitya Viveka — Discrimination Between the Eternal and Transient
The first exercise is a survey of your own life: of everything you have experienced, what has stayed. The tradition expects the honest answer to be very little.
Talks with Sri Ramana Maharshi, Talk 197
Sadhana Chatushtaya — The Four Prerequisites for Vedantic Study
Four things are asked before study begins: discrimination, dispassion, a set of virtues, and the wish for freedom. Character comes before philosophy, in that order.
Vivekachudamani 17
Karma Yoga in Advaita — Selfless Action as Purification
Selfless work has a role here, and it is a modest one: it clears the mind for inquiry. Advaita takes the teaching from the Bhagavad Gita, which it reads as scripture.
Bhagavad Gita 2.47
Karma and Jnana — Action and Knowledge
Shankara's harder claim is that action can produce purity of mind but not freedom. Doing more will not get you there, which is a strange thing to meet in a discussion of purpose.
Brahmasutra Bhashya 1.1.1
Moksha and Dharma — Liberation Does Not Negate Ethics
Recognising that all is one does not cancel right and wrong. The liberated person is described as acting well because the self-serving distortion has gone, not because a rule is being kept.
Vivekachudamani 540
Moksha as Recognition — Not Achievement
Liberation is not built up over time. It is described as noticing what was already the case, which is why the tradition speaks of recognition rather than progress.
Talks with Sri Ramana Maharshi, Talk 1
The End of Seeking
Seeking ends, on this account, not because you arrive but because the seeker turns out to be what was sought. That is a claim rather than a comfort.
Who Am I? (Jean Klein)
You Are Already That — The Complete Teaching
The whole teaching compressed: you are not on your way to becoming Brahman. Everything else in Advaita is a method for making that sentence mean something.
I Am That, Chapter 1
If you came for a direction, Advaita gives a poor one and a good question. It will not tell you which work to take, and it is specific about what the work is for: a mind steady enough to examine itself. Whether that counts as a purpose or as the dismantling of the idea is a fair thing to argue about.