**Chronological Order of Events:**

1. **Arrival of European Traders in India**
- The Portuguese were the first Europeans to reach India in 1498, led by Vasco da Gama. They established trade relations with the local rulers along the coast.

2. **The British East India Company**
- In 1600, the British East India Company was granted a charter by Queen Elizabeth I, allowing them to trade with the East Indies, including India. The company set up trading posts in various parts of India.

3. **Establishment of British Rule in Bengal**
- The Battle of Plassey in 1757 marked the beginning of British political control in India. The British East India Company defeated the Nawab of Bengal, Siraj-ud-Daulah, and gained control over Bengal.

4. **The British Raj**
- Following the Indian Rebellion of 1857, the British government took direct control over India from the East India Company. This period, known as the British Raj, lasted until India gained independence in 1947.

5. **Indian Nationalist Movement**
- Throughout the 19th and early 20th centuries, the Indian nationalist movement grew in strength, advocating for independence from British rule. Prominent leaders like Mahatma Gandhi and Jawaharlal Nehru played significant roles in this movement.

6. **Indian Independence**
- After years of struggle and non-violent resistance, India finally achieved independence on August 15, 1947. The country was partitioned into India and Pakistan, leading to massive communal violence and migration.

**Explanation:**

The establishment of European and British rule in India was a gradual process that unfolded over several centuries. European traders, starting with the Portuguese, arrived in India in the late 15th century and established trade relations with local rulers. However, it was the British East India Company that played a pivotal role in shaping British rule in India.

The British East India Company, granted a charter by Queen Elizabeth I in 1600, set up trading posts along the Indian coast. They gradually expanded their influence and established political control, particularly in Bengal. The Battle of Plassey in 1757 was a turning point, as it marked the defeat of the Nawab of Bengal by the British East India Company, leading to their political control over Bengal.

The British Raj, a period of direct British rule in India, began after the Indian Rebellion of 1857. The British government took over from the East India Company and governed India until its independence in 1947. During this time, the Indian nationalist movement gained momentum, with leaders like Mahatma Gandhi advocating for independence through non-violent means.

Finally, after years of struggle and sacrifices, India achieved independence on August 15, 1947. The country was partitioned into India and Pakistan, resulting in widespread violence and mass migration. This marked the end of British rule in India and the beginning of a new era of self-governance and nation-building.