The Communist Party of India-Marxist (CPI-M) was formed in the year 1964.

Explanation:
The CPI-M was formed through a split in the Communist Party of India (CPI), which occurred in 1964. The split was the result of ideological differences between the two factions within the CPI.

1. Ideological Differences:
The split in the CPI was primarily due to ideological differences between the two factions. One faction, led by E.M.S. Namboodiripad and P. Sundarayya, believed in adopting a more revolutionary and militant approach towards the goal of establishing a socialist society in India. They advocated for armed struggle and a more independent stance from the Indian National Congress in order to achieve their objectives.

2. Formation of CPI-M:
The other faction, led by S.A. Dange and B.T. Ranadive, held a more moderate view and believed in aligning with the Congress party and participating in parliamentary democracy. These differences in approach and ideology led to a split in the CPI, with the more revolutionary faction forming the CPI-M in 1964.

3. Emergence of CPI-M:
The formation of the CPI-M marked the emergence of a new communist party in India with its own distinct ideological stance. The CPI-M aimed to establish a socialist society through revolutionary means and advocated for a more independent and militant approach.

4. Evolution and Growth:
Since its formation, the CPI-M has played a significant role in Indian politics. It has been involved in various mass movements, trade union activities, and struggles for the rights of workers, peasants, and marginalized sections of society. The party has also been a major force in several states, including West Bengal, Kerala, and Tripura.

Overall, the formation of the CPI-M in 1964 was a result of ideological differences within the Communist Party of India. It marked the emergence of a new party with a more revolutionary and independent approach towards achieving a socialist society in India.