Advaita Vedanta holds that all of us have the same self. Then what is the concept of Moksha in Advaita Vedant ? Do people still take birth after getting Moksha?
Moksha is freedom from the endless transmigration cycle. Here are some passages explaining moksha as understood in Advaita Vedanta school.
When men of knowledge, conversant with the rules of Yoga, become as fixed as a stake of wood, and as immovable as a mountain, then are they said to be in Yoga. When one does not hear, and smell, and taste, and see; when one is not conscious of any touch; when one’s mind becomes perfectly free from every purpose; when one is not conscious of anything, when one cherishes no thought; when one becomes like a piece of wood, then is one called by the wise to be in perfect Yoga. At such a time one shines like a lamp that burns in a place where there is no wind; at such a time one becomes freed even from one’s subtle form, and perfectly united with Brahma. When one attains to such progress, one has no longer to ascend or to fall among intermediate beings. When persons like ourselves say that there has been a complete identification of the Knower, the Known, and Knowledge, then is the Yogin said to behold the Supreme Soul.
Mahabharata Santi Parva Section CCCVII
Yudhisthira on Emancipation
There are two well-known paths (for us), viz, the path of the Pitris and the path of the gods. They that perform sacrifices go by the Pitri-path, while they that are for salvation, go by the god-path. By penances, by Brahmacharya, by study (of the Vedas), the great Rishis, casting off their bodies, proceed to regions that are above the power of death. Worldly enjoyments have been styled as bonds. They have also been called action. Liberated from these two sins (viz, bonds and action) one attains to the highest end. ….As a person on the hill-top looketh down upon men on the plain below, so he that has got up on the top of the mansion of knowledge, seeth people grieving for things that do not call for grief. He, however, that is of foolish understanding, does not see this. He who, casting his eyes on visible things, really seeth them, is said to have eyes and understanding. The faculty called understanding is so called because of the knowledge and comprehension it gives of unknown and incomprehensible things. He who is acquainted with the words of persons that are learned, that are of cleansed souls, and that have attained to a state of Brahma, succeeds in obtaining great honours. When one seeth creatures of infinite diversity to be all one and the same to be but diversified emanations from the same essence, one is then said to have attained Brahma. Those who reach this high state of culture attain to that supreme and blissful end, and not they who are without knowledge, or they who are of little and narrow souls, or they who are bereft of understanding, or they who are without penances. Indeed, everything rests on the (cultivated) understanding!’
Mahabharata Santi Parva Section XVII
Bhisma/Suka on emancipation
Bhishma continued [Suka said],’..By knowledge, one attains to that whither there is no occasion for grief; whither one becomes freed from birth and death; whither one is not subject to decrepitude; whither one transcends the state of conscious existence; whither is Brahma which is Supreme, Unmanifest, immutable, ever-existent, imperceptible, above the reach of pain, immortal, and transcending destruction; whither all become freed from the influence of all pairs of opposites (like pleasure and pain, etc), as also wish or purpose. Reaching that stage, they cast equal eyes on everything, becoming universal friends and devoted to the good of all the creatures.’
Mahabharata Santi Parva Section CCXLI