It seems to be a period in US history that is often ignored, but what I do know about it, such as reconstruction, populism, the Spanish-American War, Theodore Roosevelt and the Progressives, and Gilded Age-era political corruption, suggests it was an interesting time worth learning more about.
If you're interested in the monopolies of the time I would recommend The Tycoons by Charles Morris, and The Robber Barons by Matthew Josephson. Another book I heard was good that I have not yet read is Bully Pulpit.
It's about all of Europe, Britain, and North America really, but I consider Stephen Kern's "Culture of Time and Space" to be an absolute must on that period in history (1880-1914).
Kern explores how modern industry, technology, and thought (encompassed under the broad idea of 'modernity') contributed to an alteration of human perception. He refers to "time-space compression," and how increased speeds of travel and communication fundamentally altered the manner in which people experienced time and space. His final chapter, which applies all of these theories to the "July Crisis" leading up to World War One, is fascinating.
Benjamin Singer's "Melodrama and Modernity" is a good companion work to Kern's book, as it investigates how the experience of the modern city affected art.
William Leach's "Land of Desire" is another interesting work on this period in American history. Though focusing centrally on the career of L. Frank Baum, Leach examines the spread of consumerism in America.
I saw someone mention William Cronon's "Nature's Metropolis" on this sub the other day, which is an environmental history that traces the development of Chicago in this period.
These are all cultural histories, so I'd be interested to see what people suggest in terms of more straight-up political history or social history.