Union forces comprised the equivalent of 2,047 regiments during the Civil War, of which 1,696 were infantry, 272 were cavalry, and 78 were artillery. Unfortunately, few of these have unit histories in any great detail. Frederick H. Dyer, A Compendium of the War of the Rebellion, vol. III, purports to have capsule histories of all of these regiments, and some are republished on the Internet (see, for example, the entry under Indiana Infantry Regiments). It is hoped that many more regimental histories will be published over time.
Frederick H. Dyer, A Compendium of the War of the Rebellion (originally published in Des Moines, IA : Dyer Pub. Co., 1908. A reprint edition is currently available at $125, but it should be located in many larger libraries) [Three volumes, including v.1. Number and organization of the armies of the United States -- v.2. Chronological record of the campaigns, battles, engagements, actions, combats, sieges, skirmishes, etc., in the United States, 1861-1865, and v.3. Regimental histories] or [Union regimental histories]
The Official Records [Armies] Search contents [here] or [here]
The Official Records [Navies] Search contents [here] or [here] or check excerpts [here]