Navratri ("Nav" meaning nine and "Ratri" meaning nights), These nights are devoted to the reverence of Goddess Durga (Maa Durga) who exists in many forms and is the manifestation of the absolute energy that pervades the Universe. During these days and nights prayers are offered to Mother Goddess. For the devout these days are the sacrosanct for it is during these days when Goddess Durga takes a stock of her devotees and grants all blessings, removes ills and evils and ensures unproblematic life for her devotees.
Navratri's each night is dedicated to one form of Goddess Durga. That is every ratri of the Navratri corresponds to worship of different forms of Maa Durga.
This embraces Maa Shailputri, who was the daughter of Parvatraj Himalaya (King of the Mountain), wife of Lord Shiva and mother of Ganesha and Kartikeya.
Maa Brahmachaarini- Who gives the message of pure love to the world;
Maa Chandraghanta - Who establishes Justice and wears crescent moon on Her head;
Maa Kushmaanda, Who provides the basic necessities to the world;
Skand Maa - Who gives the gift of differentiation of right from wrong to the world;
Maa Kaatyayini - Who persistently battles against the evil and deceitful entities;
Maa Kaalratri, who killed Raktabeej ( a demon who produce a demon from every drop of blood that fell from his body. Goddess eventually licked the blood before it could reach the ground and hence conquered him);
Maa MahaGauri - Who also liberate the world of evil forces;
Mata Sidhidaarti -Who is a treasure house of Mystic Powers (Yantra Tantra) and Knowledge (Gyaan).
Navaratri > http://en.wikipedia.org/wiki/Navaratri
Mysore Dasara > http://en.wikipedia.org/wiki/Mysore_Dasara
Dussehra > http://www.festivalsofindia.in/Dussehra/
Durga puja > http://www.festivalsofindia.in/durgapuja/