There's little point rehashing the plots of these stories. Instead, I'll summarise the strengths and weaknesses of the author, assuming that you are unfamiliar with his work.
First, I disagree with the previous reviewer's comparison with Agatha Christie. There is virtually no common-ground between Christie and Carr. Carr's mysteries are more in the style of the classic Ellery Queen locked-room puzzles, to be solved by logical examination of evidence, not by a pseudo-psychological analysis of the motivations of the criminal. Most of Carr's output involves an impossible crime, with no trickery on the part of the author, but lots on the part of the criminal! You never come away from a Carr novel feeling cheated, you might fail to solve it, but you still appreciate the artistry of the solution. The main difference between Christie and Carr, in my view, is that Christie was a weak writer with feeble plot development, weak characterisation, and little attempt at setting a scene. Carr, on the other hand, introduces very interesting characters, highly skilled plot development, and was an acknowledged master at creating an ambience for his work. The latter, in many cases, is crucial since his criminals commonly used misdirection, like conjurers, to divert investigators from the truth. Another strength of Carr was his attention to detail and research. Many of his books contain inline references to standard works of criminology of the time. The three novels in this book feature his detective Dr Fell, who "starred" in over 20 novels. Writing under the name Carter Dickson, Carr produced a similar number of novels featuring his other favourite sleuth, Sir Henry Merrivale.
So, if Carr produced highly readable and satisfying detective novels, what were his weaknesses? He only really has one that intrudes throughout his work. Carr was an American enamoured of pre-WW II Britain, with a particular weakness for stately homes and titles. His political views were decidedly right-wing and he can't resist quite vicious digs at things like Socialism, the Labour Party, and state-ownership. However, these are relatively few and should not be allowed to detract from the stories. Also, Carr had a penchant for humour. Often this is genuinely funny, but occasionally one has to remind oneself that times change and what was once funny, might now, rightly, be considered racist or sexist. Personally, I have no problem with this, since it seems unfair to judge work published 70 years ago by the standards of today. Finally, there is no doubt that the quality of Carr's work deteriorated towards the end of his career. This is almost certainly largely due to the effects of a crippling stroke in the early 1960s, when the author relocated to the USA. However, Carr was at this time trying to modernise his output and adapt, with some success, to changing times. So some of the criticism of his later works comes from disaffected Carr "purists".
In summary, Carr was an author of considerable ability, whose best work is regarded as a pivotal contribution to the genre. The three stories collected here are above average contributions from his early period.