What's that, you say? You want further reading on one of the most devastating wars in modern history, South America's greatest international conflict? As someone who just did all this research: good freaking luck.
The problem isn't "there are no good books on this war", there ARE. If you want to learn about the Paraguayan War, you have three real options. Good luck finding any of them easily.
The best and most accessible book on the Paraguayan War is Chris Leuchars, To the Bitter End. Excellent, gripping, comprehensible, not too long. And seriously: good luck getting your hands on this one. I was lucky to get a library copy, and I had to do Inter-library loan. Copies of this book on the Internet run to about $100. This is the problem with researching obscure wars: only a few books have been published, and because no one reads them, they have limited print runs, so there aren't many copies of the books that DO exist.
Another very accessible book is Charles Kolinski's Independence or Death. This book was the first real history of the Paraguayan War in the English language, though since it was published in 1965 it IS a bit dated. Bigger problem: good luck finding a copy! Most of them run about $50. I was able to get one copy for about $30, and it has been INVALUABLE for describing these armies as they went to war.
Finally, the most comprehensive and complete history of the Paraguayan War is Thomas Whigham's two volumes cited below. Together these run to about a thousand pages of history, which is PERFECT for me but may get very tedious for anyone else. Combined, these two very thick...but luckily very easy to find...volumes run about $100 combined.
So yeah. All these books are great, but they're hard to find and expensive when you do because of their rarity. Such is the cost of researching unknown soldiers. But don't worry: my podcast is free, and having taken a look at the other stuff out there...my series on the Paraguayan War will be the most accessible and most comprehensive take on this conflict that you are literally going to ever run across.
Sometimes a historical niche needs filling. And I guess I can be the one to fill it.
SOURCES
Esposito, Gabrielle. The War of the Triple Alliance. Point Pleasant, NJ: Winged Hussar Publishing, 2017.
Fausto, Boris, and Sergio Fausto. A Concise History of Brazil. 2nd Ed. Cambridge, UK: Cambridge University Press, 2014.
Hooker, Terry D. The Paraguayan War. Nottingham: Foundry Books, 2008.
Kolinski, Charles J. Independence or Death! The story of the Paraguayan War. Gainesville, Florida: University of Florida Press, 1965.
Kraay, Hendrik; Whigham, Thomas L. I Die with My Country: Perspectives on the Paraguayan War, 1864–1870. Dexter, Michigan: Thomson-Shore, 2004.
Leuchars, Chris. To the Bitter End: Paraguay and the War of the Triple Alliance. Westport, Connecticut: Greenwood Press, 2002.
Rees, Sian. The Shadows of Elisa Lynch. London: Headline Review, 1986.
Rock, David. Argentina, 1516-1987: From Spanish Colonization to Alfonsin. Berkeley: University of California Press, 1986.
Saeger, James Schofield. Francisco Solano Lopez and the Ruination of Paraguay: Honor and Egocentrism. Lanham, MD: Rowan and Littlefield, 2007.
Scheina, Robert. Latin America's Wars: The Age of the Caudillo, 1791–1899. Brassey's: Dulles, 2003.
Thompson, George (1869). The War in Paraguay: With a historical sketch of the country and its people and notes upon the military engineering of the war. London: Longmans and Green, 1869.
Washburn, Charles. The history of Paraguay : with notes of personal observations, and reminiscences of diplomacy under difficulties (2 vols). Lincoln, Nebraska: University of Nebraska Press, 1871.
Whigham, Thomas L. The Paraguayan War: Causes and Early Conduct. Vol. 1. Lincoln, Nebraska: University of Nebraska Press, 2002.
Whigham, Thomas L. The Road to Armageddon: Paraguay versus the Triple Alliance, 1866–70. Calgary, AB: University of Calgary Press, 2017.
Williams, John Hoyt. The Rise and Fall of the Paraguayan Republic, 1800-1870. Austin: University of Texas Press, 2014.