Casino Royale was written by Ian Fleming as the first ever James Bond book in 1953. Ian was a commander who worked with naval intelligence in the war - he really did lead a life of high stake gambling in exotic locations. He wrote this book from his homestead 'Goldeneye' in Jamaica.
When Bond first meets some French agents, he orders for them. The guy gets a 'fine a l'eau' - a classic cocktail of Cognac and water. The girl gets a 'Bacardi' (rum, my favorite brand). It doesn't say that James gets anything for himself. The first drink we see James drink is a straight whisky 'on the rocks' (quotes theirs) in his room.
Next, in the casino, we get the first ever description of his classic drink. Here's the verbatim text from the book:
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'Bond insisted on ordering Leither's Haig-and-Haig 'on the rocks' [a quality Scotch whiskey - Lisa] and then he looked carefully at the barman.
'A dry martini,' he said. 'One. In a deep champagne goblet.'
'Oui, monsieur.'
'Just a moment. Three measures of Gordon's [an English gin - Lisa], one of vodka, half a measure of Kina Lillet. [this is NOT vermouth - see below!] Shake it very well until it's ice-cold, then add a large thin slice of lemon peel. Got it?'
'Certainly, monsieur.' The barman seemed pleasant with the idea.
'Gosh that's certainly a drink,' said Leiter.
Bond laughed. 'When I'm ... er ... concentrating.' he explained, 'I never have more than one drink before dinner. But I do like that one to be large and very strong and very cold and very well-made. I hate small portions of anything, particularly when they taste bad. This drink's my own invention. I'm going to patent it when I can think of a good name.'
He watched carefully as the deep glass became frosted with the pale golden drink, slightly aerated by the bruising of the shaker. He reached for it and took a long sip.
'Excellent,' he said to the barman, 'but if you can get a vodka made with grain instead of potatoes, you will find it still better.'
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A short while later when he's sharing a carafe of vodka, nestled in a bowl of crushed ice, with the female agent, he learns her name is Vesper. He says:
'Can I borrow it?' He explained about the special martini he had invented and his search for a name for it. 'The Vesper,' he said. 'It sounds perfect and it's very appropriate to the violet hour when my cocktail will now be drunk all over the world. Can I have it?'
Lillet and Vermouth
Note that some claim that Kina Lillet is a vermouth. It is NOT A VERMOUTH :) My research shows Lillet Kina is a wine based drink that has quinine in it. Kina refers to the Kina Kina (quinquina) tree where quinine comes from. In fact back in the James Bond days it was VERY bitter and the entire drink would have been quite bitter. They changed the formula in the mid-80s to have less quinine, and now it comes in 'Lillet Blanc' and 'Lillet Rouge'. They're made in Podensac, in France. Technically they are 'French aperitif wines'. They are a blend of wine grapes, oranges, orange peels and quinine.
Vermouth, on the other hand, is a fortified wine - i.e. wine kicked up with heavy alcohol. They then add in herbs and spices. The main types of vermouth are dry vermouth, sweet red vermouth, and white vermouth.