The first book in this series stands alone. The next three must be read in sequence; they should not really be separate books at all. The fifth is a sequel and stands alone.
This is some of the most gripping fiction I've read in any genre. The characters are real right down to their scars and buttons. The plots are convoluted and the action is furious. The theme is interspecies politics in a technological society a few hundred years hence.
There is an uneasy balance between Pyanfar Chanur's race, the bipedal cats that call themselves hani, and several other alien races. Things are complex enough at home, but out in space things are downright Byzantine. They trade, but they also poach and harass and maneuver and sometimes things get ugly. The different races have highly incompatible societies, and Pyanfar often has to make split-second decisions despite nearly complete ignorance of the internal politics and culture of the other races. Some of them are almost completely incomprehensible, like the methane-breathing Knnn who communicate in matrices of ideographs.
Now Pyanfar has discovered a human---a specimen of a completely unknown race. The addition of a new race to the political mix is bound to make things unstable.
The surface story is terrific, but one of the things I enjoyed the most about the series is the sexual politics of the hani. Hani males are drones who fight over breeding rights back home while the females trade throughout known space. Pyanfar has upset hani society by taking a male into space and teaching him the ropes. In a rather delicious and subtle pastiche of human society, Pyanfar fights an uphill battle trying to convince her peers that yes, men can be good for something---only their cultural conditioning makes them appear to be useless, not their genetic makeup.
From the author's homepage:
Pyanfar's motto is, when confronted with vastly intelligent, aggressive politics: Do something totally irrational and let the enemy think himself to death.
This series is related to several other crackling good Cherryh books like Downbelow Station, Forty Thousand in Gehenna, Heavy Time, and many others. They are all great reads.