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

Detail Description
The syllable Om is referred to as praṇava. Other used terms are akṣara (literally, letter of the alphabet, imperishable, immutable) or ekākṣara (one letter of the alphabet) and omkāra (meaning literally
"Om syllable", and connoting: a beginning and female divine energy). Udgitha, a word found in Sama Veda and bhasya (commentaries) based on it, is also used as a name of the syllable. The word has three phonemes: "a-u-m", though it is often described as trisyllabic despite this being either archaic or the result of translation.

The syllable Om is first mentioned in the Upanishads, the mystical texts associated with the Vedanta philosophy. It has variously been associated with concepts of "cosmic sound" or "mystical syllable" or "affirmation to something divine", or as symbolism for abstract spiritual concepts in the Upanishads. In the Aranyaka and the Brahmana layers of Vedic texts, the syllable is so widespread and linked to knowledge, that it stands for the "whole of Veda". The etymological foundations of Om are repeatedly discussed in the oldest layers of the Vedantic texts (the early Upanishads). The Aitareya Brahmana of Rig Veda, in section 5.32, for example suggests that the three phonetic components of Om (pronounced AUM) correspond to the three stages of cosmic creation, and when it is read or said, it celebrates the creative powers of the universe. The Brahmana layer of Vedic texts equate Om with Bhur-bhuvah-Svah, the latter symbolizing "the whole Veda". They offer various shades of meaning to Om, such as it being "the universe beyond the sun", or that which is "mysterious and inexhaustible", or "the infinite language, the infinite knowledge", or "essence of breath, life, everything that exists", or that "with which one is liberated". The Sama Veda, the poetical Veda, orthographically maps Om to the audible, the musical truths in its numerous variations (Oum, Aum, Ovā Ovā Ovā Um, etc.) and then attempts to extract musical meters from it.

The syllable Om evolves to mean many abstract ideas in the earliest Upanishads. Max Müller and other scholars state that these philosophical texts recommend Om as a "tool for meditation", explain various meanings that the syllable may be in the mind of one meditating, ranging from "artificial and senseless" to "highest concepts such as the cause of the Universe, essence of life, Brahman, Atman, and Self-knowledge".