While there are a great many mysteries and thrillers about serial killers, there are surprisingly few of them among the classic mysteries. Agatha Christie's "The A.B.C. Murders" comes to mind, and Ngaio Marsh's "Singing in the Shrouds," but few others. That's one of the reasons why I think "Cat of Many Tails" is one of Ellery Queen's most interesting and successful novels. Over the course of a blazingly hot summer in New York City, Ellery Queen (the detective - it's always confusing when the author uses his character's name as his own pen name!) and his father, Inspector Richard Queen, are faced with a series of seemingly random murders. There are next to no clues, and the investigators are almost forced to sit and wait for each crime in the hope that the criminal will be careless.
"Cat of Many Tails" has a rather ambiguous ending, something that became pretty common in later Queen novels. I think it's one of the better written novels in the series. It's the subject of today's Classic Mysteries podcast, and you can hear the whole review here. As you will see, if you click the title link above, it's pretty much out of print, as is the case with all Ellery Queen novels, but I'm going ahead and putting it on the podcast bAmazon has links to a number of booksellers offering reasonably-priced copies. It's also available from the Mystery Guild, and if you belong to that book club, you might want to order a copy of "Queen's Ransom," which includes "Cat of Many Tails" along with "The Roman Hat Mystery" and "Calamity Town." It's a good introduction to the Queen novels.