Coalition Government:
A coalition government is a form of government where political parties from different ideologies come together to form a governing body. In a coalition government, multiple parties agree to share power and work together to run the administration. This is usually done to form a stable government when no single party has gained an absolute majority in an election.

Formation of Coalition Government at the Center:
The first coalition government at the center in India was formed in 1977, after the end of the Emergency period imposed by the Indira Gandhi-led Congress government. This coalition government was known as the Janata Party government.

During the 1977 elections, the opposition parties came together under the banner of the Janata Party to challenge the Congress party's dominance. The Janata Party, a coalition of various parties including the Bharatiya Jana Sangh, the Socialist Party, and the Congress (O), emerged victorious and formed the government.

The Janata Party government, led by Morarji Desai, comprised a diverse group of politicians with different ideologies. It faced numerous challenges during its tenure, including internal conflicts and disagreements on various policy matters. Eventually, the coalition government collapsed due to internal rifts, leading to fresh elections in 1980.

This marked the beginning of a trend of coalition governments in Indian politics. Subsequently, several coalition governments have been formed at the center, with different parties joining hands to gain a majority and form a government.

In recent years, coalition governments have become more common as the political landscape has become more fragmented, with no single party able to secure a clear majority. Coalition governments provide an opportunity for different parties to work together, negotiate policies, and share power. However, they also have challenges, such as the need for constant coordination and compromise among coalition partners.

In conclusion, a coalition government is a political arrangement where multiple parties join forces to form a governing body. The first coalition government at the center in India was formed in 1977, known as the Janata Party government. This marked the beginning of a trend of coalition governments in Indian politics, with different parties coming together to gain a majority and form governments at the center.