The Chronicles of Barsetshire are a collection of six books (I've made it through five already) published between 1855-1867. Each book involves different central characters, but all the stories take place in the same fictional county created by Trollope. Rather than review each book I've already read in the series, I want to talk about the series as a whole. Trollope is a great writer and his style, which I find unique to the time period he published in, is what makes this series most attractive.
The series consists of The Warden, Barchester Towers, Doctor Thorne, Framley Parsonage, The Small House at Allington, and The Last Chronicle of Barset. While, it's helpful to read the books in order - since once characters are introduced they're frequently referred to - it's not a must.
While the focus of each book is really on the various relationships between members of the county, Trollope also takes a stance on important issues of the day - particularly political parties, the state of the church, and how the social structure throughout England affects personal relationships. Making it through almost the entire series by now, I've found the stories and character struggles very interesting. The most unique feature of these books is the author's voice itself. Trollope is actually a character, butting into the narrative to support and guide the reader. Trollope does everything from warning his readers that there won't be one central hero to a story to reassuring us that because he hates suspense, he won't leave the reader guessing about the fate of his more beloved characters.
Trollope also uses unconventional methods to conclude his stories. While his characters mostly end up happy, all the stories don't conclude with everyone married to their true love and all the poor characters wealthy. Our Warden (who appears primarily in the first two books) repeatedly refuses positions within the Church that would allow him to live comfortably financially. The women in The Small House at Allington don't all get to marry their true love. Characters die leaving perfectly good wives widowed. These elements of reality make Trollope more like Hardy than Austen (if you were looking for a comparison.)
The pictures Trollope paints throughout this series of a particular county and all its characters is very vivid. He wants you to see this place as he sees it, so he digs deeply into detail when talking about specific places and people. If you're a fan of "classic" literature and enjoy books from this period (like the Bronte sisters and Dickens) Trollope might be worth a try. Give The Warden a shot and see what you think.