With which of the following social reform movements is Ishwar Chandra Vidyasagar most prominently associated?

The correct option is Advocating and legalizing widow remarriage.

Detailed Explanation:

1. Historical Background:
Ishwar Chandra Vidyasagar (1820–1891) was one of the most eminent social reformers, educationalists, and key architects of the 19^th-century Bengal Renaissance.

2. Crusade for Widow Remarriage:
During the 19^th century, child marriage was widespread in India, leaving many young girls widowed at an early age and subjected to severe social ostracization. Vidyasagar dedicated himself to reforming these conditions. Using deep scholarship, he referenced ancient Hindu scriptures (notably the Parasara Smriti) to argue that Hindu traditions did not prohibit widow remarriage.

3. Enactment of the Law:
Vidyasagar filed petitions signed by hundreds of supporters to the Legislative Council. His tireless campaign directly led to the passing of the Hindu Widows' Remarriage Act, 1856 (Act XV of 1856), legalizing widow remarriage and declaring children born of such marriages legitimate.

4. Evaluation of Other Options:
- Spearheading agrarian revolts: Vidyasagar was an intellectual, author, and social reformer, not a leader of peasant rebellions.
- Exclusively promoting western English-medium schooling: Vidyasagar strongly advocated for vernacular Bengali education alongside English and Sanskrit, and composed foundational Bengali text primers such as Borno Parichay.
- Organizing militant revolutionary groups: Vidyasagar pursued social transformation strictly through education, writing, legislative reform, and philanthropic work, rather than militant activity.

Hence, Ishwar Chandra Vidyasagar is most prominently associated with advocating and legalizing widow remarriage.