There's a recent biography:

John B. Freed, Frederick Barbarossa: The Prince and the Myth (Yale University Press, 2016)

There are also a couple of older English ones:

Peter Munz, Frederick Barbarossa: a Study in Medieval Politics (Cornell University Press, 1969)

Karl J. Leyser, Frederick Barbarossa and the Hohenstaufen Polity (University of California Press, 1988)

And some translations of primary sources:

Charles Christopher Mierow, trans., Otto of Freising and his Continuator Rahewin, The Deeds of Frederick Barbarossa (Columbia University Press, 1953, repr. 1966)

Graham Loud, trans., The Crusade of Frederick Barbarossa: The History of the Expedition of the Emperor Frederick and Related Texts (Ashgate, 2010)

There's not as much about Frederick I as there is about Frederick II since, well, he's not as interesting...but this should be a good start, I hope!