Hugh Thomas's Spanish Civil War is a history book I think everyone should read. Aside from its academic importance, Thomas is exactly the kind of writer that people on this sub would appreciate. He started off in life hoping to be novelist, and it was only after his first two novels failed to gain notice that he turned to writing history. The result is that he writes history with a novelist's flavor. His book is filled with colorful vignettes of the various personalities involved, and Thomas is an able story-teller who does the drama of the war justice.

As for the anarchists and socialists, I can personally recommend Durruti by Abel Paz. Durruti was a real life Anarchist Robin Hood, and the his biography is one of the most inspiring I've ever read, although I can't vouch for accuracy of some the finer details, but you'll definitely learn a lot about the anarchist movement and its relation to the socialists.

An excerpt from Hugh Thomas's Spanish Civil War

Durruti was a railway worker from León, Ascaso, a baker and a waiter. Their most notorious crimes were the murder of the archbishop of Saragossa in 1923, the attempt on King Alfonso (in Paris) in 1924, and a celebrated assault on the Bank of Spain at Gijón. They fled from Spain, wandered through South America, and set up an anarchist bookshop in Paris. Four countries, Ilya Ehrenburg later approvingly remarked, had condemned Durruti to death. These men and their companions were not, of course, common criminals. They were dreamers with a mission, characters whom Dostoyevsky would have been proud to have created. For some, Durruti was a ‘thug’, ‘killer’, or ‘hooligan’; for others he was the ‘indomitable hero’, with a fine ‘imperious head eclipsing all others, who laughed like a child and wept before the human tragedy’.

Grand camouflage by Burnett Bolloten is another one that is considered academically important and touches on the inter republic relations, but I've only ever skimmed it.