GANESHJI
Ganesha, also spelled Ganesa or Ganesh and also known as Ganapati, Vinayaka, and Pillaiyar, is one of the best-known and most worshipped deities in the Hindu pantheon. His image is found throughout India. Hindu sects worship him regardless of other affiliations. Devotion to Ganesha is widely diffused and extends to Jains, Buddhists, and beyond India.

Although he is known by many other attributes, Ganesha's elephant head makes him easy to identify. Ganesha is widely revered as the Remover of Obstacles and more generally as Lord of Beginnings and Lord of Obstacles (Vighnesha, Vighneshvara), patron of arts and sciences, and the deva of intellect and wisdom. He is honoured at the start of rituals and ceremonies and invoked as Patron of Letters during writing sessions.

(Source: http://en.wikipedia.org/wiki/Ganesha).
 

DURGA

In Hinduism, Durga or Maa Durga (Mother Durga) is a form of Devi, the supreme goddess. Goddess Durga is considered by Hindus to be the mother of Ganesha, and Kartikeya. She is thus considered the fiercer, demon-fighting form of Shiva's wife, goddess Parvati.

Durga is depicted as a warrior aspect of Devi Parvati with 10 arms who rides a lion or a tiger, carries weapons and assumes mudras, or symbolic hand gestures. This form of the Goddess is the embodiment of feminine and creative energy (Shakti).

The Great Goddess Durga is said to be exquisitely beautiful. Her form is blindingly bright (devi), with three lotus-like eyes, ten powerful hands, lush hair with beautiful curls, a red-golden glow from her skin and a quarter moon on her forehead. She wears a shiny oceanic blue attire emitting fierce rays. Her ornaments were carved beautifully of gold, with ocean pearls and precious stones embedded in it. Each god also gave her their own most powerful weapons: Rudra's trident, Vishnu's discus, Indra's thunderbolt, Brahma's kamandalu, Kuber's Ratnahar, etc. Himalayas gifted her a fierce white and gold lion. On the end of the eighth and beginning of the ninth day of waxing moon, Chanda and Munda came to fight the goddess. She turned blue with anger and the goddess Chamunda leaped out of her third eye. Her form was the most powerful one with three red eyes, blood-filled tongue and dark skin; she finally killed the twin demons with her sword. This form of the divine goddess is worshiped during the sandhikshan of Durga Puja festival, as sandhi/chandi puja. Finally, on the tenth day of waxing moon, Durga killed Mahishasura with her trident.

The word Shakti, meaning sacred feminine force, and Durga reflects the warrior aspect of the goddess, embodying a traditional male role. She is also strikingly beautiful, and initially Mahishasura tries to marry her. Other incarnations include Annapurna and Karunamayi (karuna = kindness). Durga's darker aspect Kali is represented as the consort of god Shiva, on whose body she is often seen standing.

According to the narrative from the Devi Mahatmya of the Markandeya Purana, the form of Durga was created as a warrior goddess to fight a demon. The demon's father Rambha, king of the demons, once fell in love with a water buffalo, and Mahish Asur (the demon Mahish) was born out of this union. He is therefore able to change between human and buffalo form at will (mahish means "buffalo"). Through intense prayers to Brahma, Mahishasur had the boon that he could not be defeated by any man or god. He unleashed a reign of terror on earth, heaven and the nether worlds.

Eventually, since only a woman could kill him, the Holy Male Trinity went down to the river Ganges and prayed the mantra, "Om Namo Devaye", imploring of the great goddess Devi to save their realm from ruin. They were blessed with her compassion when the goddess Durga was born out of the river.

The four day long Durga Puja is the biggest annual festival in Bengal, Orissa and Bihar. It is celebrated likewise with much fervour in other parts of India, especially the Himalayan region, but is celebrated in various forms throughout the Hindu universe.

The day of Durga's victory is celebrated as Vijaya Dashmi.

The actual period of the worship however may be on the preceding nine days (Navaratri) followed by the last day called Vijayadashami in North India or five days in Bengal (from the sixth to tenth day of the waxing-moon fortnight). Nine aspects of Durga known as Navadurga are meditated upon, one by one during the nine-day festival by devout Shakti worshippers.

In North India, the tenth day, signifying Rama's victory in his battle against the demon Ravana, is celebrated as Dussehra - gigantic straw effigies of Ravana are burnt in designated open spaces (e.g. Delhi's Ram Lila grounds), watched by thousands of families and little children.

In Gujarat it is celebrated as the last day of Navaratri, during which the Garba dance is performed to celebrate the vigorous victory of Mahishasura-mardini Durga.

The Goddess Durga is worshiped in her peaceful form as MahaGauri, The Fair Lady, Shree Shantadurga also known as santeri, is the patron Goddess of Goa. She is worshiped by all Goan Hindus irrespective of caste and even by some Christians in Goa.

Goddess Durga is worshiped in many temples of Dakshina Kannada district of Karnataka.

(Source: http://en.wikipedia.org/wiki/Durga)