Gaņeśa from the name we understand that it’s the deity

of the gaņas, head of the gaņas.

Rgveda contains an invocatory prayer addressed to a
deity named Gaņapati, the word Gaņapati comes twice to
refer Br̦haspati. In the 10th Maņd̦ala, the word is used with
reference to Indra.
In Maitrāyaņi Samhitā reference is made to Gāņapatyas, i.e.
worshippers of Gaņapati.
Gaņapati is also referred as Hastimukha, Danti. The
Taittirīya Āraņyaka & the Nārāyaņa Upanishad refer to
Vakratuņd̦a,Danti etc. In the Gaņeśa Atharva-shirsha, he is
referred as Ekdanţa, Vakratuņd̦a & Danti.
Manava-Grhya mentions four Vinayakas who obstruct
human activities viz; Salakatankata,
Kusmandarajaputra, Usmita and Devayajana.
Mita, Sammita, Sala, Katankata, Kusmanda, Rajaputra
in Yajnavalkya Smriti
In the Baudhāyana-Dharma-Sūtra, Gaņapati is referred
as Vighna, Vināyaka, Sthūla, Hastimukha, Vakratuņd̦a,
Ekdanţa & Lambodara.
In the Yājñvalkya-smriti, Vināyaka is appointed as Chief
of Śiva’s Gaņas.
Alexander’s historian Niarches describe about Mushaka
tribe, Elephant tribe; he suggested that Mushaka &
elephant are the gods of tribal, these people wearing mask
of elephant.
In 9th-10th Cen. A.D. a epic Gaņeśa Puraņa & Gaņapati
Stotra describes ritual of Gaņeśa & how he connected to
Śiva & Pārvati. Gaņeśa is manasik putra of Śiva
Gaņa suggested the place in 6th cen.B.C. where there are
some Mahājanapadas & the chief called Gaņādhyakshya.
Gaņeśa was a very famous god in India, China, Japan,
Java, Sumatra, Malaysia, Borneo, Thailand, Afghanistan,
SriLanka, Mexico.
There are 5 important cults:
1) Śaiva cult
2) Vaişņava cult
3) Śaktī cult
4) Saura cult &
5) Gaņpatya cult.
 Riddhi & Siddhi are two consorts of Gaņapati.
Both are daughters of Brahma. Riddhi means
prosperity & Siddhi means achievement.
 In earlier times Gaņeśa is considered as
Brahmachari in Northern India.
 Buddhism & Jainism also accepted this god.
Coomarswamy suggested that Gaņeśa is originated from
the cult of Yaksha. R.S.Gupte suggested him as a god of
Harvest, rat used as pesticides in farm & Gaņeśa controls
rat. In Sarnath one sculptural evidence of Gaņeśa
seated on rat in 6th-7th Cen. A.D.
Pingulavadan Tantra-Manuscript discovered in Nepal,
dated around 12th Cen. A.D., pictorial representation of
Gaņeśa in red colour, seated on rat of blue colour &
holding Axe & Tusk.
Hindu tradition-in the earliest known references
like Aitarēya-brāhmaņa, Gaņapati is identified with
Brahmā, Brahmaņaspati or Bŗihaspati. Concern of Gaņeśa
with Bŗihaspati the teacher of gods & Gaņeśa’s one name
is Bŗihaspati.
Mudgal Rishi written Gaņapati Stotra, its basic
philosophical book of Gaņapatya cult & he claim
Gaņapati as an important god with 32 forms e.g.
BālaGaņapati, SiddhiGaņapati, Veer Gaņapati, Simha
Gaņapati etc.
Earlier period he was an obstacle but later in 6th-7th
Cen.A.D. he was benevolent god, the destroyer of
obstacle.
Gaņapati is closely associated with the Jainism &
Buddhism also, in Jainism he is associated with Saraswati
the goddess of knowledge Gaņeśa seems to have been
included in the Jain pantheon during 7th-12th century
A.D.; Aparajita the Buddhist goddess dancing on Gaņeśa
& Tantric Gaņapati in Buddhist literature known as
Heramba. Also worshipped in the very beginning of
Buddhist rituals.
1st evidence of Gaņeśa on coins of Huvishka.
2nd evidence on Allahabad pillar inscription of
Samudragupta-he conquered king Gaņapati.
1st iconic representation at Bhumra on outdoor
pannel of Gaņapati with his gaņas.
2nd iconic representation in Udaygiri Vidisha district-
Gaņeśa placed with Vishnu-clear inscription of Gupta
King Chandragupta IInd dated 439 A.D.
3rd iconic representation from Bhitargaon, not
separate temple but Gaņapati is a semi-god. Basic
iconic representation of Gaņeśa with big belly, axe &
Modak.
9th- 10th Cen.A.D. he is coming in Panćayatan
temple structure e.g. Śiva is main god then other four
are Pārvati, Gaņeśa, Skanda & Nandi.
In Rūpamaņd̦ana it is stated that, in a temple,
dedicated to Gaņeśa, there should be on the left of the
image of this deity the figure of Gajakarna; on the
right, of Siddhi; to the north, of Gauri; to the east, of
Buddhi; to the south-east, Bālachandra; to the south, of
Sarasvati; to the west, of Kubera; & at the back, of
Dhūmraka.
The trunk of this elephant-head god shown turned
towards the left or in some cases it towards the right.
His image may have four, six, eight, ten or sixteen
arms; but majority of images have four arms.
The belly of Gaņeśa as he is called Lambodara has
to be very capacious. Due to the big belly the legs
show the right leg as bent & make it rest vertically
on a seat.
On the chest a snake has in the form of the
yajñōpavīta; & another snake should serve as a belt
going round to the belly.
Gaņeśa is figured in most cases with only two
eyes; the āgamas prescribe three eyes to him.
He is represented as seating in Padmāsana or a mouse
or in rare instances, a lion; the standing image of
Gaņapati is in samabhaṅga or in dvibhaṅga ,
tribhaṅga etc.
SOME DEPICTION OF GAŅEŚA

 The image
photograph is
representation from
Mathura dated 5th
Cen.A.D., Gaņeśa in
standing pose, two
hands, big belly.
The photograph from
Nachna (M.P.), outer
part of temple; left
hand in varad mudra
& right hand holding
snake; dated 4th-5th
Cen. A.D.
From Nachana-Gupta Period-Seating in
Ardhaparyankasana-right hand holding Bijpurak-
Nagabandh on belly.
From Gangaikodcholpuram, late
Pallava dynasty, dated 7th
Cen.A.D.-Nritya Gaņeśa-
pedestal have musicians, one is
clapping, one is singing & the
other is playing instrument-
snake band on belly, left hand
free for dancing pose, right hand
holding Modak, upper right
hand holding Axe & upper left
holding Broken tusk.
6th- 7th Cen.A.D.,
seating in
Ardhaparyankasan
on ornamented
pedestal, some
ornamentation
appeared- left hand
holding Modaka,
right holding
Broken tusk-
bajubandh (armlet)
in arms.
The image from Gujarat,
late Gupta period, 6th Cen.
A.D.- standing in
dvibhaṅga, very thin &
transparent cloth appeared
here depicted very
realistically-pearl design on
head-dress, snake band on
his right side, both hands
broken-one devotee is
depicted on the left &
Gaņeśa placed his hand
on the shoulder of the
devotee.
Representation of
Gaņeśa in iconic form
in proper Devakoshtha
.Here he placed as
semigod
, Aihole idol, dated 6th
Cen.A.D.-seated in
ardhaparyankasana,
lower left holding
Modak , upper left
holding Paraśu, lower
right holding Broken
tusk, upper right
holding Ankuśa-
abstract
representation of
Nagabandh.
Paramāra period-nritya mudra-elaborate representation-
nagabandh on belly-left lower hand in dancing position
placed on left thigh, upper left holding Ankuśa in the form
of Śakti, right lower hand holding Paraśu & right upper
also in dancing posture.
Śakti Gaņeśa or Siddhi
Gaņeśa-shows similarity
with Śiva-Pārvati icon-right
upper hand of Gaņeśa
holding Śakti’s finger
&lower right holding broken
tusk, upper left holding
Śakti- Gaņeśa is seating in
Ardhaparyankasana & on
his left lap Śakti is seating.
10 handed Gaņeśa-10th Cen.A.D.-
Khajuraho- made in Sandstone- made in
different pattern-he is considered as an
important god.
11th Cen.A.D.-
Sandstone- very fine
piece of sculpture,
glaze on stone-
nrityamudra-first
time appearance of
rat holding Modak.
From Hampi, Vijaynagar
empires patronage, 15th
Cen.A.D.
Snake band attributed
continuously, quite large in
size, seated on pedestal.
First time placed in separate
semi-sanctum.
 Abroad Images

Afghanistan-5th-6th Cen.A.D. Java- 7th Cen.A.D.

Nepal-11th-12th Cen.A.D. SriLanka-12th Cen.A.D.
Java and Cambodia
East Java
 China
Borneo
Besides this sculptural representation, there are
some Bronzes & paintings also represent Gaņeśa
in iconic form.
Among them Chola bronzes are well-known for
the depiction of the icons.
We also have evidences of painting of Gaņeśa
1) From Tanjor- a painting on glass-dated 18th Cen.A.D.-two
flying creatures shown in painting resembling foreign
influence.
2) The other is from Maisore-an oil painting- dated 19th
Cen.A.D.
Most accepted opinion is that cult of Gaņeśa
appeared sometime in the late Gupta period.
By the 10th century, the god was worshipped by an
independent sect known as Gaņapatya.
The sect came to have as many as six sub-divisions,
worshipping respectively Maha-Ganapati, Haridra-
Ganapati, Ucchistha-Ganapati, Navanita-Ganapati
and Samtana-Ganapati.
At present practice, Gaņeśa is the god whom the
pious Hindu “invokes when he begins all sacrifices &
religious ceremonies, all addresses even to superior
gods, all serious compositions in writing, & all wordly
affairs of moment.”
References:
1)Elements of Hindu Iconography – Vol.I:: Part I
by T.A.Gopinatha Rao
2)Iconography of the Hindus, Buddhists And Jains
by R.S.Gupte
3)GAŅEŚA-A Monograph On The Elephant-Faced God
by Alice Getty