Ganesha Purana, Incarnations of Ganesha

                Ganesha Purana is an upapurana that includes mythology, cosmogony, genealogy, metaphors, yoga, theology and philosophy relating to Ganesha. The text is organized in two voluminous sections, the Upasanakhanda or "section on devotion" has 92 chapters, and the Kridakhanda or "section on the divine play” has 155 chapters. The Kridakhanda is also called the Uttarakhanda. The text's composition and expansion date has been estimated to be the late medieval period, between the 13^th to 18^th centuries.

                   The Upasanakhanda, presents two modes of worship. One is meditation and mystic contemplation of Ganesha as the eternal,  presented in vedanta school of Hindu philosophy, the metaphysical absolute and Paramatma (Nirguna, supreme spirit), where he is same as the aatma (soul, innermost self) within oneself. The second approach is through preparing an image of god (Saguna, murthi), decorating it with flowers, presenting it offerings and festively remembering him in pooja-style homage. The Upasanakhanda presents these ideas in a series of episodically stories and cosmogony that weaves in ancient mythologies as dynamic empirical reality and presents Ganesha as the absolute unchanging reality. 

                     The Kridakhanda narrates the stories of four incarnations of Ganesha, each for the four different yugas. The 155 chapters of this section are separated into the four Yugas. Chapters 1 through 72 present Ganesha in Krita Yuga, chapters 73 through 126 present Ganesha in the Treta Yuga, while chapters 127 through 137 present Ganesha in Dwapara Yuga. Chapters 138-48 constitute the Ganesha Gita, which is modeled on the Bhagavad Geeta, but adapted to place Ganesha in the divine role. The discourse is given to King Varenya during Ganesha's incarnation as Gajanana. The Ganesha Gita shows that ninety percent of its stanzas are, with slight modifications, taken from the Bhagavad Gita.  Their topics are the same: karma yoga, jnana yoga and bhakthi yoga. It is followed by a short section on Kali Yuga in chapter 149. The rest of chapter 149 through chapter 155 is interlocutory, following the literary requirements of a valid Puranic genre. 

Ganesha as Vinayaka in Krita Yuga, with ten arms, huge, very generous in giving gifts and riding a lion

Ganesha as Mayuresvara in Treta Yuga, with six arms, with a white complexion and riding a peacock

Ganesha as Gajanana in Dwapara Yuga, with four arms, a red complexion and riding a mouse

Ganesha as Dhumraketu in Kali Yuga, with with two arms, of smoke complexion, mounted on a horse