A martini is gin and vermouth, shaken and served up with a twist or olives (though I had a waitress once tell me a martini did not include olives - now THAT'S a purist!). The exact right proportion of vermouth is critical. The modern attitude that one can get the vermouth by simply looking towards France completely misses the point.
Hemingway liked his martinis with a 15:1 gin:vermouth ratio. As late as the 1930s, a martini would have been 4:1, with a couple drops of orange bitters. I think somewhere around 7:1 is perfect...at that proportion, it becomes something more than just gin and vermouth.
A martini does not include vodka. And a martini is CERTAINLY not one of these sugar-laden promoters of tooth decay that is garishly colored and served in a cocktail glass. Gfunkdave has spoken.