The novel, The Sinister Shadow, finds Savage with three of his operatives involved in the case of a criminal called the Funeral Director. The Funeral Director is capturing wealthy men and ransoming them, killing his victims with a gas which induces a heart attack. The Funeral Director's most recent hostage is Lamont Cranston, which complicates matters considerably because Cranston is very important to the mysterious personage called the Shadow; moreover, the Funeral Director is an old enemy of the Shadow and is determined to learn his foe's true identity.
Perhaps because Doc Savage and the Shadow both originated in prose fiction this is the medium to which they are best suited. Murray writes The Sinister Shadow as though it were being published in the 1930s - not in the manner of pastiche, but simply obeying the narrative conventions which Savage and the Shadow belong to. The story is full of familiar faces from the pulps, most notably in the Shadow's supporting cast.
To some extent, this book is actually a Shadow novel; it takes a while for the Shadow to come to the fore, but when he does the novel is all but his - it tends to follow he and his agents rather than Savage, particularly as the villain and his intended victim are both Shadow characters. For much of Savage's investigation the Shadow is a complicating factor as Savage doesn't understand how the Shadow is connected to Cranston, nor if the Shadow truly exists. When Savage and the Shadow finally meet up the duo are forced to compromise in order to work together as neither approves of the other's methods - the Shadow kills his foes while Savage brainwashes his and gives them new identities.
Considering so much of Doc Savage's DNA was used to create Superman and the Shadow to create Batman, it's interesting that Savage and the Shadow have a complicated relationship much like their comic book inspirations, but there is no homage to Superman & Batman found in this book - Doc Savage and the Shadow are icons in their own right.
This is the first Doc Savage novel I've read; I can't speak to whether Doc Savage fans will enjoy it, but Shadow fans - wow, get this one now!