Hayagriva is depicted with 4 armed, carrying a Conch & Wheel known as Shanka and chakra in His two hands, a rosary (aksha-mala) in the third and his fourth is in the vyakhya mudra. He is also found holding the vedas in some occasions. Hayagreeva is associated with the purity of knowledge and is represented in the same way as Saraswati. White is a symbolism of purity that is depicted in the "white horse" face he adorns

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HAYAGREEVA AVATAR (Incarnation as Hayagreeva) : Once Lord Brahma becoming tired of his creative activities, he was in need of some rest. The night of the Brahma was approaching. Given his fatigue, Lord Brahma yawned. All the four Vedas came out from his open mouth. A demon who used to live near him in disguise, abducted the Vedas. Lord Vishnu took his sixteenth incarnation as Hayagreeva to protect the Vedas. In this incarnation, his face resembled that of a horse and the rest of his body resembled that of Sri Narayan with all of his four hands. He killed the demon and protected the Vedas.

Hayagreeva is an incarnation of Vishnu with the horse head and is believed to be the storehouse of knowledge. Agasthya is one of the great sages of yore who is one of the stars of the constellation great bear. At his request Hayagreeva taught him the most holy 1000 names of Lalitha. It is also lord Hayagreeva who gave the two famous Devi Stotras - Lalita Sahasranama Stotra & Lalita Trishati stotras to Agastya Muni

(Lalitha Sahasranama is in the 36th chapter of Lalitopakyana in Brahmanda Purana. It is presented in the form of instructions imparted to the sage Agasthya by Hayagriva who is an incarnation of Sri Maha Vishnu. )

Hence the Saligrama with typical horse mane like marks is Known as Hayagreeva Shila. Worship of Lord Hayagreeva is very auspicious for all types of knowledge and learning

Thiruvahindrapuram has one of the most ancient temples dedicated to Lord Sri Hayagriva.

The rough English phonetic version of the Hayagriva stotra, the first two stanzas of the Shloka is given below:
Njaananandamayam Devam , Nirmalam Spadikakrutham |
Aadaram Sarva Vidhyaanaam, Hayagreevam Upaasmahe |

Vidyaarambam (the first step of learning) begins with a prayer to Sri Hayagreeva, praising him as the presiding deity for all knowledge. May He grant us the power to imbibe this knowledge & wisdom we seek with the recitation of this mantra.