The Indian Puranas present a vivid description of creation (sristi). In this connection they introduce the concept of anda, the cosmic egg in the vast stretch of water out of which the four-faced Brahma originates for carrying out the rest of the actual creation of the universe. Similarly, for carrying out the process of dissolution of the universe in a reverse order, the concept of Rudra as a deity entrusted with the physical task of dissolution is brought in. What is created needs to be well preserved and protected until the stage of dissolution. For this purpose, a third deity, Lord Vishnu is admitted. The Pancharatra treatises which also deal with the cosmology advance the theory of emanation and bring in the three Vyuha manifestations of the Supreme Being - Samkarsana, Pradyumna and Aniruddha- for explaining the three major cosmic functions of creation, sustenance and dissolution.
In order to accommodate the three other deities, Brahma, Vishnu and Rudra, introduced by the Puranas, the Pancharatra system speaks of two stages of creation, i.e., primary and secondary. The three vyuha deities are put in charge of the three cosmic functions at the first stage and the Puranic deities are entrusted with the three cosmic functions at the second stage.
From the philosophical point of view, Brahman is the primary cause of the universe (jagat kararja) as emphasised in the Taittiriya Upanishad and the second aphorism of Vedanta. Brahman, as the metaphysical ground of the universe, is responsible for creation, sustenance and dissolution. Even if other deities actually perform these three functions, it is Brahman as their antaratma or in-dweller controlling them from within that causes the different cosmic functions.
Thus discussed above is the process of the creation of the Universe according to the Vaishnava belief system.