Like the Ganesha Purana, the Mudgala Purana considers Ganesha to represent the ultimate reality of being. As such, Ganesha's manifestations are endless but eight of his incarnations (Sanskrit:अवतार; avatāra) are of most importance. The eight incarnations are introduced in MudP 1.17.24-28. The text is organized into sections for each of these incarnations. These are not the same as the four incarnations of Ganesha that are described in the Ganesha Purana.
The incarnation described in the Mudgala Purana took place in different cosmic ages. The Mudgala Purana uses these incarnations to express complex philosophical concepts associated with the progressive creation of the world. Each incarnation represents a stage of the absolute as it unfolds into creation. Granoff provides a summary of the philosophical meaning of each incarnation within the framework of the Mudgala Purana: Along with the philosophy, typical Puranic themes of battles with demons provide much of the story line. The incarnations appear in the following order:
1. Vakratunda (Vakratuṇḍa) ("twisting trunk"), first in the series, represents the absolute as the aggregate of all bodies, an embodiment of the form of Brahman. The purpose of this incarnation is to overcome the demon Matsaryāsura (envy, jealousy). His mount (vāhana) is a lion
2. Ekadanta ("single tusk") represents the aggregate of all individual souls, an embodiment of the essential nature of Brahman. the purpose of this incarnation is to overcome the demon Madāsura (arrogance, conceit). His mount is a mouse.
3. Mahodara ("big belly") is a synthesis of both Vakratuṇḍa and Ekadanta. It is the absolute as it enters into the creative process. It is an embodiment of the wisdom of Brahman. The purpose of this incarnation is to overcome the demon Mohāsura (delusion, confusion). His mount is a mouse.
4. Gajavaktra (or Gajānana) ("elephant face") is a counterpart to Mahodara. The purpose of this incarnation is to overcome the demon Lobhāsura (greed). His mount is a mouse
5. Lambodara ("pendulous belly") is the first of four incarnations that correspond to the stage where the Purāṇic gods are created. Lambodara corresponds to Śakti, the pure power of Brahman. The purpose of this incarnation is to overcome the demon Krodhāsura (anger). His mount is a mouse
6. Vikata (Vikaṭa) ("unusual form", "misshapen") corresponds to Sūrya. He is an embodiment of the illuminating nature of Brahman. The purpose of this incarnation is to overcome the demon Kāmāsura (lust). His mount is a peacock
7. Vighnaraja (Vighnarāja) ("king of obstacles"), corresponds to Viṣṇu. He is an embodiment of the preserving nature of Brahman. The purpose of this incarnation is to overcome the demon Mamāsura (possessiveness). His mount is the celestial serpent Śeṣa.
8. Dhumravarna (Dhūmravarṇa) ("grey color") corresponds to Śiva. He is an embodiment of the destructive nature of Brahman. The purpose of this incarnation is to overcome the demon Abhimanāsura (pride, attachment). His mount is a horse.