How the dissolution of the universe takes place?

There are two types of dissolution of the manifested cosmos. At the end of every 4,320,000,000 solar years, when Brahma, the lord of one particular universe, goes to sleep, there is one annihilation. And at the end of Lord Brahma’s life, which takes place at the end of Brahma’s one hundred years of age, in our calculation at the end of 8,640,000,000 x 30 x 12 x 100 solar years, there is complete annihilation of the entire universe, and in both the periods both the material energy called the mahat-tattva and the marginal energy called jiva-tattva merge in the person of the Supreme Lord. The living beings remain asleep within the body of the Lord until there is another creation of the material world, and that is the way of the creation, maintenance, and annihilation of the material manifestation. The material creation is effected by the interaction of the three modes of material nature set in action by the Lord, and therefore it is said here that the Lord existed before the modes of material nature was set in motion. In the Sruti-mantra it is said that only Vishnu, the Supreme Lord, existed before the creation, and there was no Brahma, Shiva or other demigods. Vishnu means the Maha-Vishnu, who is lying on the Causal Ocean. His breathing, only all the universes are generated in seeds and gradually develop into gigantic forms with innumerable planets within each and every universe. The seeds of universes develop into gigantic forms in the way seeds of a banyan tree develop into numberless banyan trees.

This Maha-Vishnu is the plenary portion of the Lord Sri Krishna, who is mentioned in the Brahma-samhita as follows:
“Let me offer my respectful obeisances unto the original Personality of Godhead, Govinda, whose plenary portion is the Maha-Vishnu. All the Brahmas, the heads of the universes, live only for the period of His exhaling after the universes are generated from the pores of His transcendental body.” (Brahmasamhita 5.58) Thus Govinda, or Lord Krishna, is the cause of Maha-Vishnu also. The ladies talking about this Vedic truth must have heard it from authoritative sources. An authoritative source is the only means of knowing about transcendental subject matter definitely. There is no alternative. The merging of living beings into the body of Maha-Vishnu takes place automatically at the end of Brahma’s one hundred years. But that does not mean that the individual living being loses his identity. The identity is there, and as soon as there is another creation by the supreme will of the Lord, all the sleeping, inactive living beings are again let loose to begin their activities in the continuation of past different spheres of life. It is called suptotthita naya, or awakening from sleep and again engaging in one’s respective continuous duty. When a man is asleep at night, he forgets himself, what he is, what his duty is and everything of his waking state. But as soon as he awakens from slumber, he remembers all that he has to do and thus engages himself again in his prescribed activities. The living beings also remain merged in the body of Maha-Vishnu during the period of annihilation, but as soon as there is another creation they arise to take up their unfinished work. This is also confirmed in the Bhagavad-gita (8.18-20). The Lord existed before the creative energy was set in action. The Lord is not a product of the material energy. His body is completely spiritual, and there is no difference between His body and Himself. Before creation, the Lord remained in His abode, which is absolute and one.

Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, First Canto, Chapter 10 – Text 21