Iconography
Representations of Ganesha show wide variations and distinct patterns changing over time. He may be portrayed standing, dancing, heroically taking action against demons, playing with his family as a boy, sitting down or on an elevated seat, or engaging in a range of contemporary situations.

Ganesha has the head of an elephant and a big belly. This statue has four arms, which is common in depictions of Ganesha. He holds his own broken tusk in his lower-right hand and holds a delicacy, which he samples with his trunk, in his lower-left hand. The motif of Ganesha turning his trunk sharply to his left to taste a sweet in his lower-left hand is a particularly archaic feature. A more primitive statue in one of the Ellora Caves with this general form has been dated to the 7th century.[38] Details of the other hands are difficult to make out on the statue shown. In the standard configuration, Ganesha typically holds an axe or a goad in one upper arm and a noose in the other upper arm.

Associations
Obstacles
Ganesha is Vighneshvara or Vighnaraja, the Lord of Obstacles, both of a material and spiritual order. He is popularly worshipped as a remover of obstacles, though traditionally he also places obstacles in the path of those who need to be checked. Paul Courtright says that "his task in the divine scheme of things, his dharma, is to place and remove obstacles. It is his particular territory, the reason for his creation."

Krishan notes that some of Ganesha's names reflect shadings of multiple roles that have evolved over time. Dhavalikar ascribes the quick ascension of Ganesha in the Hindu pantheon, and the emergence of the Ganapatyas, to this shift in emphasis from vighnakart? (obstacle-creator) to vighnahart? (obstacle-averter). However, both functions continue to be vital to his character, as Robert Brown explains, "even after the Pur??ic Ga?e?a is well-defined, in art Ga?e?a remained predominantly important for his dual role as creator and remover of obstacles, thus having both a negative and a positive aspect

Buddhi (Knowledge)

Ganesha is considered to be the Lord of letters and learning. In Sanskrit, the word buddhi is a feminine noun that is variously translated as intelligence, wisdom, or intellect. The concept of buddhi is closely associated with the personality of Ganesha, especially in the Puranic period, when many stories stress his cleverness and love of intelligence. One of Ganesha's names in the Ganesha Purana and the Ganesha Sahasranama is Buddhipriya. This name also appears in a list of 21 names at the end of the Ganesha Sahasranama that Ganesha says are especially important. The word Priya can mean "fond of", and in a marital context it can mean "lover" or "husband", so the name may mean either "Fond of Intelligence" or "Buddhi's Husband"

Frist Chakra
According to Kundalini yoga, Ganesha resides in the first chakra, called Muladhara (m?l?dh?ra). Mula means "original, main " adhara means "base, foundation". The Muladhara chakra is the principle on which the manifestation or outward expansion of primordial Divine Force rests.[95] This association is also attested to in the Ganapati Atharvashirsa. You continually dwell in the sacral plexus at the base of the spine. Thus, Ganesha has a permanent abode in every being at the Muladhara. Ganesha holds, supports and guides all other chakras, thereby "governing the forces that propel the wheel of life"

Youtube Mantra Link

Conch The right-turning white conch shell represents the beautiful, deep, melodious, interpenetrating and pervasive sound of the dharma, which awakens disciples from the deep slumber of ignorance and urges them to accomplish their own welfare for the welfare of others	Endless knot The endless knot denotes "the auspicious mark represented by a curled noose emblematic of love" . It is a symbol of the ultimate unity of everything. Moreover, it represents the intertwining of wisdom and compassion, the mutual dependence of religious doctrine and secular affairs, the union of wisdom and method, the inseparability of śūnyatā "emptiness" and pratītyasamutpāda "interdependent origination" , and the union of wisdom and compassion in enlightenment. This knot, net or web metaphor also conveys the Buddhist teaching of interpenetration. It is also an attribute of the god Vishnu, which is said to be engraved on his chest. A similar engraving of the Shrivatsa on the historical Gautama Buddha's chest is mentioned in some lists of the Physical characteristics of the Buddha.	Pair of Golden FishThe two golden fish symbolise the auspiciousness of all sentient beings in a state of fearlessness without danger of drowning in saṃsāra. The two golden fishes are linked with the Ganges and Yamuna nadi, prana and carp:
LotusThe lotus flower , represent the primordial purity of body, speech, and mind, floating above the muddy waters of attachment and desire. The lotus symbolizes purity and renunciation. Although the lotus has its roots in the mud at the bottom of a pond, its flower lies immaculate above the water.	ParasolThe jewelled parasol , which is similar in ritual function to the baldachin or canopy: represents the protection of beings from harmful forces and illness. It represents the canopy or firmament of the sky and therefore the expansiveness and unfolding of space and the element æther. It represents the expansiveness, unfolding and protective quality of the sahasrara: all take refuge in the dharma under the auspiciousness of the parasol.	VaseThe treasure vase represents health, longevity, wealth, prosperity, wisdom and the phenomenon of space. The treasure vase, or pot, symbolizes the Buddha's infinite quality of teaching the dharma: no matter how many teachings he shared, the treasure never lessened.
DharmaChakraThe Dharmachakra or "Wheel of the Law" represents Gautama Buddha and the Dharma teaching. This symbol is commonly used by Tibetan Buddhists, where it sometimes also includes an inner wheel of the Gankyil. Nepalese Buddhists don't use the Wheel of Law in the eight auspicious symbols.	Vicoty BannerThe dhvaja "banner, flag" was a military standard of ancient Indian warfare. The symbol represents the Buddha's victory over the four māras, or hindrances in the path of enlightenment. These hindrances are pride, desire, disturbing emotions, and the fear of death. Within the Tibetan tradition, a list of eleven different forms of the victory banner is given to represent eleven specific methods for overcoming defilement. Many variations of the dhvaja's design can be seen on the roofs of Tibetan monasteries to symbolise the Buddha's victory over four māras. Banners are placed at the four corners of monastery and temple roofs. The cylindrical banners placed on monastery roofs are often made of beaten copper.