The obvious place to start reading on the Battle of Adrianople is the longest and most comprehensive primary account of the battle by Ammianus Marcellinus. Ammianus was an old soldier himself and was writing not too long after the events and so is generally regarded as a reliable source.

The best modern discussion of the battle, and the one that overturned the Nineteenth Century myth that it was largely a victory of heavy cavalry over outdated infantry, is Thomas S. Burns' article "The Battle of Adrianople: A Reconsideration" (Historia, 22, 1973, pp. 336-45). By analysing the primary accounts, looking at the evidence regarding Gothic use of cavalry and estimating the amount of fodder available to cavalry in the area at that time of year, Burns makes it clear that there is no evidence that the Gothic army was substantially mounted. This was an infantry battle in which a key role was played (largely by chance) by the Gothic army's small cavalry wing.

More recently, Simon Macdowall's Adrianople - AD 378: The Goths Crush Rome's Legions (Osprey Campaign 84: Oxford, 2001), gives a good summary of the current thinking on the battle, with plenty of background and context, some photos of the probable battlesite, maps of the campaign, diagrams of the way the battle unfolded and colour plates of late Roman troops and Gothic warriors in action.
Cheers,
Thiu