The Delhi Public Library, Shastri Bhavan (closest metro station to it is Central Secretariat) and the Archaeological Survey of India (closest metro station is Rajiv Chowk) are all free of charge, if you want to access some books and material. For more info, read our library guide here. Also, membership to these libraries are around INR 20 and - respectively.
Timings:
The Delhi Public Library: 8am to 8pm
Archaeological Survey of India: 9:30am to 6pm (is closed on the weekend)