Final answer:
The Vesper martini was first introduced in Ian Fleming's novel 'Casino Royale', the first book featuring James Bond, published in 1953.
Step-by-step explanation:
The novel where the Vesper martini was first mentioned is 'Casino Royale', which was written by Ian Fleming. This book, published in 1953, is the first novel featuring the now-iconic character James Bond, who is known for his preference for martinis 'shaken, not stirred.' Inventing the Vesper martini was part of characterizing James Bond's unique and sophisticated tastes, setting the standard for Bond's many other distinctive preferences that would follow in Fleming's subsequent novels and the later film adaptations.