This is one of my favorites. The main character for the first 4 books is Pyanfar Chanur, of the species Hani. She is the captain of a private trading ship, "The Pride of Chanur" (usually shortened to "the Pride") in Compact Space.
There are a handful of species in Compact space, which doesn't include humans. The 3 methane breathing species have the most technologically advanced ships and share space stations, but communication is nearly impossible--Only one will communicate understandably to oxygen breathers, and they somewhat translate for the others.
The oxygen breathers are diverse. The Hani are feline, with a social structure similar to a pack of lions. Males are the head of clans, with leadership determined by physical prowess. Hani are the most recent species in space, and their society has not yet adapted. A clan leader will have several wives. Many adult males will not survive, and males are not considered stable enough to do useful work. As a result, only the Hani women are in space.
The Mahendo'sat are primates, and are responsible for bringing Hani to space.
Stsho are non-violent to the point of hiring guards from other species. When threatened they will "phase"--Their personality will fragment and they will become a different person, without the memories of their previous personality. They are essentially the economic leaders of the Compact.
The Kif society is based on competition, without the concept of loyalty. A Kif leader who finds himself losing will often be killed by his crew who will then join the winning side. This is considered proper in Kif society. They prey on other species when possible.
The first book (The Pride of Chanur) is a stand-alone story. Tully, the first human in Compact space escapes from the Kif and takes refuge in The Pride. Pyanfar refuses to give him back. This sets off a war with a faction of the Kif, who destroy several uninvolved Hani ships and set The Pride running and manipulating, trying to save both clan and species interests.
The second (Chanur's Venture), third (The Kif Strike Back) and fourth (Chanur's Homecoming) books are a single story-Don't start one unless you've got all three. The Pride is trying to recover from incidents in the first book. At the end of the first book, Pyanfar's husband was defeated and chased off his estate. Pyanfar brings him to space, the first male Hani. Tully returns --This time making contact with the Mahendo'sat who secretly turn him over to Pyanfar. Kif threaten the Hani homeworld, and Pyanfar is the only one able to deal with this threat.
The fifth book is a standalone, some time after the first 4. Pyanfar has become one of the Compact's most important people. Her niece Hilfy is now the clan leader, and has her own ship, "Chanur's Legacy". Male Hani are starting to venture into space. The Legacy picks up a male Hani that has been abandoned by its crew, and take a very complex contract to deliver a Stsho artifact, without fully understanding the contract written in Stsho. The terms wind up sending The Legacy on a wild goose chase with a Stsho passenger. One of the things I like is that this book doesn't try to be even more intense and important than the previous ones. The first 4 books had the potential of wiping out the entire Hani species if things went wrong. The fifth book is primarily around the survival of the Legacy and the Chanur clan--Still intense and fast paced, but not artificially enhanced.
Complaints: Humans and Stsho need to be drugged to deal with hyperspace. Hani who have never met humans have compatible drugs available in appropriate dosages, without experimentation.
The scale doesn't feel interplanetary. Space stations hold a couple hundred ships at most. The shops have a feel of bazaar or flea market. The feeling is that there are a few thousand sentients in space. With this scale, space transport would be limited to luxury goods, but they mention carrying bulk food as well.
The fifth book was obviously written after the author became aware of computer viruses and trojans, and avoiding these is a minor and distracting plot point.
The final complaint is the organization of the omnibus editions of the book. It contains the first three novels of the series instead of the more logical arrangement that would contain the second story complete.
A good thing is that you can use the first book as a sample-If you are like me, a book has to be really bad before I'll abandon it before the end. Here you can get a good sample of the style in one book. If it doesn't suit, you can stop after the first.