Lord Ganesha represents Wisdom, Spirituality & Prosperity. He has two consorts namely Riddhi, Siddhi & two sons Shubh, Labh. His two upper arms carry Noose and Elephant Goud (in some cases Axe). One of his lower arm is shown in Abhay mudra (Ashirwad) while he carries a bowl full of Modaks in other lower arm. Noose is used by him to catch the straying minds of his devotees and set them back to the course while he uses Goad to steer souls to right path away from ignorance and earthly illusions. Bowl full of Modak represents the ultimate & the sweetest goal which is Moksha.
There are eight incarnations of Lord Ganesha which are collectively called 'Ashta Vinayaka' & represented in temples which are self originated. The names of each of them are:- Moreshwar, Mahaganapati, Chintamani, Girijatmak, Vigneshwar, Siddhivinayak, Ballaleshwar & Varad Vinayak. These temples are located around Pune, Ahmednagar, Raigad district. The Ashta Vinayaka yatra begins at Moreshwar which is located in Morgaon near Pune.
Bij Mantra:- Om Gang Ganapataye Namah
Before you begin something new:- Om Gan Ganpataya Namo Namah, Shri Siddhi Vinayak Namo Namah, Ashta Vinayak Namo Namah, Ganpati Bapa Moriya.
To remove obstacles while in your endevours:- Shree Vakratunda Mahakaya Surya Koti Samaprabha Nirvighnam Kuru Me Deva Sarva Kaaryeshu Sarvada.
To praise the lord:- Om Shri Ganeshaya Namah
In case of any danger or negative energy - Chant "Om Kshipra Prasadaya Namah" . This will safeguard you from all dangers and negative energy by creating a positive aura around yourself.