For Capoeira (admittedly, a somewhat niche martial art), I particularly recommend Ring of Liberation: Deceptive Discourse in Brazilian Capoeira by J. Lowell Lewis and A Street-Smart Song: Capoeira Philosophy and Inner Life by Nestor Capoeira.
Based on eighteen months of intensive participant-observation, Ring of Liberation offers both an in-depth description of capoeira—a complex Afro-Brazilian martial art that combines feats of great strength and athleticism with music and poetry—and a pioneering synthetic approach to the analysis of complex cultural performance.
I will add a caveat that it has been pointed out that this is one of many cases where a white academician has stepped in to "interpret" a piece of culture related to black people, and not everyone agrees with some of his assertions, such as the tie between headbutts and headstands, and the porter culture of Brazil, but I still think it's one of the better looks at the style from an outside perspective.
A Street-Smart Song delves into the boundless philosophical depths of capoeira, the fascinating synthesis of Brazilian dance and self-defense. Drawing from a wide range of sources—the streets of Salvador and Rio de Janeiro, the teachings of the old masters Pastinha, Bimba, and Leopoldina, and the brutal economic realities inflicted on the poorest of Brazil—Nestor Capoeira paints an indelible portrait of this living art, its spiritual heritage, and its vital place in a world hypnotized by media and crushed by poverty. The traditional poems and songs of capoeira are here, along with the author’s lively discussions of everything from the space age and television’s impact on third world culture to Candomble and capoeira’s life-changing lessons. Rounding out this absorbing cultural survey are historical photos, sketches of weapons and instruments, and fully illustrated fighting movements, taught step by step.
Considered to be one of the better explorations of Capoeira from someone from the culture. While parts of the book did come from Nestor Capoeira's dissertation, it's done in a much more conversational style. It was preceded by two other books, The Little Capoeira Book and Capoeira: Roots of the Dance-Fight-Game. One minor criticism occasionally leveled at the book is that it definitely emphasizes a particular style of "old school Capoeira" and specifically builds up the mestres associated with that style while ignoring others. Also, the translation leaves a bit to be desired.