Do Souls advance after each life?

Yes indeed!

Enlightened being explains how the journey of Soul happens,
1.from a total dormant stage where there is no knowledge or no vision at all, and
2.then develops from one-sensed to five-sensed living being and advances upto human form, and
3.finally attains liberation.

There are 3 divisions in this world:

1.Living beings who have not entered into the worldly cycle, as yet (they are called Nigod). Before the living being enters into the worldly cycle, there is this initial stage wherein there is a total covering on the Soul. The Soul is not spoilt at all, just that it is completely covered (with dense layers of coverings of karma sitting over it) such that not a single ray of light (of knowledge which is the inherent property of every Soul) of Soul is able to come out. Such living beings are called Nigod. There are infinite Souls in this stage, the dormant stage where not a single sense has been developed as yet.

2.Worldly living creatures. The Souls then advance and come into the world. In this division, the Souls gradually advance from one-sensed to five-sensed and upto human form. These beings are in bondages (of karma coverings over the Soul). When only a little covering from over the Soul of the Nigod gets removed, little light of Soul comes out and one sense gets developed. With this, the particular living being begins his journey in this world, and gradually develops from one-sensed to two-sensed, three-sensed, four sensed, five-sensed and then comes into human life-form where his mind, intellect, ego gets developed.

Suppose we take a block of wood. A lot of mud is stuck onto it, and then we put it into a pond of water. It will sink right down, isn’t it? Now, as the mud keeps dissolving, the block of wood will gradually come up. When all of the mud is removed, the block will float on water. This is how the coverings on the Soul also dissolve. And as the coverings dissolve life after life, the Souls advance in their journey.

One after another, the coverings open up; and accordingly one is born as a one-sensed, then after many many lifetimes it advances into two-sensed, then again after millions of lifetimes it advances into a three-sensed living being. One keeps taking experience and goes on rising higher in development. Until one comes in human form, it is all a natural development. From the human life-form, one can again become an animal eg. a donkey or a fish, or can go to heaven as a celestial being, or even goes in hell. It is all scientific circumstantial evidence. There is no fault of anybody. One circumstance pushes another, and another circumstance pushes the third, the coverings break and further development happens.

Finally, when one attains Self-Realization, his wandering in four life-forms stops. The worldly development completes there; new karmas stop being charged then; and when discharge of all old karmas finish, one attains liberation!

3.Liberated Souls. These Souls have already reached the stage of ultimate salvation. And therefore, they are never going to come back now in this world again and take a new life. They have reached the final stage of advancement where they are free from all the worldly bondages. Whenever one Soul from this world attains liberation, one Soul from the Nigod advances and comes into this world as a one-sensed living being– such is the law of Nature!
Hope this answers your question!

Now that we are born as a human, to advance further and complete the journey of our Soul, we must remain keen to attai
Self-Realization.

We are fortunate to have been born in an age where we have Akram Vignan. Through this spiritual science of Akram Vignan, one can attai
Self-Realization directly from the Living Gnani Purush, in a just 2-hours ceremony of Gnanvidhi, wherei
Gnani, with his divine powers, destroys the coverings of the deluding karma sitting over our Soul, and enlightens our Soul!!! Gnanvidhi is an invaluable scientific Self-Realization process, conducted out of sheer compassion for the advancement of our Soul; hence it is totally free of cost!

So now, our highest priority ought to be to get Self-Realized and advance on the path of liberation.

To know more: https://www.dadabhagwan.org/self-realization/