From a mostly military (but also somewhat cultural) perspective, Lester Grau & Dodge Billingsley's Fangs of the Lone Wolf is a series of annotated vignettes from Chechen fighters, detailing various engagements between Chechen insurgent groups and Chechen & Russian security forces. It's fairly military & tactics focused, but the vignettes often reveal some insight into the culture & general lived experiences of the combatants.