Internet Archive has many digitized books related to Providence County History and cities in Providence County, Rhode Island.
County Histories generally give information on the settlement of an area, geography, government, and industry in an area, and sometimes include biographical sketches of citizens or other information about the local residents. Some even include genealogies.
Providence County Histories and histories of cities, peoples, and organizations in Providence County, Rhode Island include:
History of Providence County, Rhode Island, Volume 1, published 1891
History of Providence County, Rhode Island, Volume 2, published 1891
Burrillville; As It Was, And As It Is, published 1856
The Early Records of the Town of Portsmouth, published 1901
History of the Town of Smithfield, published 1881