Lord Ganesha is the most widely worshipped and best known Hindu God. His image can be found throughout in India and Nepal. Hindu sects or denominations worship him regardless of affiliations. Devotion to Ganesha is diffused widely and extends to Buddhists, Jains and beyond India. He is considered as the first of gods, so he is worshipped at the start of any action or venture. He is honoured at the beginning of rituals and ceremonies and invoked as patron of letters during writing sessions. Lord ganesha is considered as the remover of obstacles of his devotees, and hence he is called as Vigneshwara, vignam means obstacles. Lord Ganesha is known by many attributes, but his elephant head makes him easy to identify, he has an elephant head and four arms. He holds the paasam(noose) and ankusam in his upper two hands and in the lower two hands holding abhaya and varada mudras. He is fond of various sweets and fruits and hence has huge belly. He generally has seated, standing and dancing postures. Ganesha is revered as the remover of obstacles, and more generally as a a Lord of Beginnings and Lord of Obstacles. He is the patron of arts and sciences, the deva of intellect and wisdom.

Lord Ganesha is considered as a bachelor, but some schools say he has two shakthis namely Siddhi and Buddhi. Siddhi is the representation of Success and Prosperity where as Buddhi represents Wisdom. His vahana is a Mooshikam or minjur(tiny mouse). Several texts relate mythological anecdotes associated with his birth and exploits and explain his distincy iconography.

Some of his names:
Ganapathi - head of Shiva ganas
Gajanana - the one with elephant face
Vigneshwara - the one who removes obstacles
Pillaiyaar
Vinayagar

Ganesha Gayathri mantram
om tat purushaaya vidmahae
vakra dhundaaya dheemahi
tanno dhandhi: prachodayaat

Brahma - Lord of creation

Brahma one of the trinity is the Lord of creation & is assisted in this process by his consort Saraswathi, who is the possessor of ultimate knowledge. Together, they thus introduce the soul into the cycle of life; 

Brahma was said to be born from the navel of Lord Vishnu at the end of one cycle to begin a fresh creation. He has four heads (originally five), representing the four vedas which are said to have sprung from his heads. His four heads are also said to represent the four yugas. He is bearded & his eyes are closed in meditation. He sits on a lotus & his vahana is the swan. In his four arms he holds the vedas, the kamandalam (water pot), suruva (sacrificial spoon) & a mala. He is a serene soul and is the provider of all sources of knowledge & wisdom. 

There are no temples for Brahma (except the ones in Rajasthan & Orissa) as for Siva & Vishnu, for there has been no separate cult for Brahma as the Saiva or Vaishnava cult. According to mythology, he is supposed to have been cursed by Shiva (for his having uttered a lie & for his ego) that he would go without worship. Yet in all Siva & Vishnu temples, there is an image of Lord Brahma on the northern wall & he is one of the important Parivara devata (attendant deity). 

Vedic Gods

Tales in Rig Veda mention about a lot of Vedic Gods. Vedic priests believed in ceremonies & rituals, which were offered to calm down these Gods. None of the Vedic God has been considered the Supreme God. In fact, different Gods have been considered as Supreme at different times, attributing the powers & qualities of one to another. Apart from Gods who have been attributed specific characteristics, several inanimate objects, qualities, emotions & various forms of nature had also been deified & worshipped.  

The earliest accepted Gods were   
Dyaush-pita (the sky father),   
Prithivi mata ( the earth mother),   
Vayu (the wind God),   
Parjanya (the rain God),   
Surya (the sun God),   
Varuna (the God of oceans),   
Agni (the fire God),   
Indra (the war God),   
Soma (the God of speech, deity of soma creeper),   
Ushas (the Goddess of dawn),   
Yama (the God of death),   
Adityas (a group of deities, who are six in number in the Rig Veda, eight in most of the Brahmanas & twelve in the Satapatha Brahmana,   
Aswini (twin Deities),   
Rudras (eight in number),   
Vasus (eight in number),   
Visvedevas ( ten in number).  

Lord Vishnu, the second Trinity finds a secondary place in the Rig Veda.