This sounds like a large topic, and how in-depth you need to search would depend on what aspects you're interested in. Consider this answer a starting point.
You can search for papers and other resources at eSocialSciences, which aims to "be a promoter of rigorous research in the social sciences and humanities on (and largely in) India and South Asia."
NGOHome is a networking and information-sharing site for NGOs in Kolkata. It also includes an online West Bengal NGO database.
Some individual NGOs operating in Kolkata include the following (you can find more by using the database mentioned above, or search in Google with keywords like intitle:ngo kolkata):
- The Kolkata Socio Cultural Research Institute works toward "women empowerment to make them self sufficient and healthy for a better tomorrow in the society."
- Paschim Banga Krira-o-Janakalyan Parishad (PBKOJP) is a Kolkata-based social welfare organization (supported in part by NGOs from Ireland, the UK, and France) "with special emphasis on street and working children, sex workers and their children, platform children and the children of other marginalized sections of society."
- Southern Health Improvement Samity (SHIS), which has an office in Kolkata, has a vision that includes the goal of "[a]chiev[ing] a value oriented sustainable society based on social orientation, economic growth, local capacity building and empowerment of people for a complete social transformation."
sample articles (found using keywords like kolkata OR calcutta AND ngo OR nongovernmental organization with parentheses as needed):
books: