See "A Brief history of the Tenth Michigan Cavalry" by Luther S. Trowbridge. It is only 44 pages long and is on Ancestry.com if you are a member. A couple libraries in Michigan have it, and the archives in Lansing. I saw it at the main Library in Detroit, but it is in their archives. It is not a very big book at all. About 4X6 and 44 pages. I am very familiar with that regiment. They spent most of their time in Tennessee. They were a part of the Tennessee Governor's Guard which was commanded by General Alvan Gillem. I wrote a book on that brigade but I did not mention the michigan hardly, as my main focus was the 9th Tennessee cavalry, of which my ancestors were a part of. I google search of the regiment brings up a summary of their service. You're best bet is the Official Records.