Modern gimlet

For ➊
6 cl gin
1 cl lime juice*
1 cl simple syrup (1:1, sugar:water)
lime wheel for garnish

Add all ingredients to a cocktail shaker.
Add ice and shake until chilled.
Strain into a chilled coupe or cocktail glass. (Add a splash of soda, if wanted).
Garnish with a lime wheel.

*Before fresh juice was standard in cocktails, Rose’s Lime Cordial was the traditional substitute for simple syrup and lime juice. Some still insist that a gimlet is not a gimlet without Rose’s, but we prefer to use fresh citrus whenever possible.

This cocktail was created for English sailors as a way to prevent scurvy. It used Rose’s Lime Cordial, lime juice mixed with syrup, to add vitamine C. This preventative drink turned out to be delicious as well. Modern Rose’s Lime Cordial is a much sweeter concoction than the original and should be replaced by fresh juice. Replace the sugar in the syrup with stevia, if wanted.

A very fino martini

For ➊
4 cl Bombay gin*
0.5 cl fino sherry

Stir gin and sherry over ice-cubes in a mixing glass.
Strain the drink (without ice!) into a pre-cooled cocktail glass. Garnish with a lemon twist.

*Optionally, replace gin with top vodka.
**Some recipes recommend 4 cl gin  + 2 cl manzanilla or fino

Red negroni

For ➊
4 cl gin
4 cl Campari
4 cl sweet (red) vermouth

In a mixing glass, add ingredients and cracked ice. Stir for at least 15 s.
Strain into a chilled cocktail glass.
Twist an orange peel and garnish.

The negroni was invented in Florence, Italy in 1919, at Caffè Casoni. Count Negroni invented it by asking the bartender, Fosco Scarselli, to strengthen his favorite cocktail, the americano, by adding gin rather than the normal soda water.
The 'negroni sbagliato' ("wrong negroni" in Italian) uses sparkling wine (e.g., prosecco) instead of gin.
Negroski is a recipe with vodka again as substitute for gin.
Cardinaloski is a negroski with some angostura drops.
Punt e Mes negroni instead replaces standard red vermouth with a specific, distinctively more bitter-tasting brand called Punt e Mes.
The cin cyn uses Cynar an artichoke based liquor, instead of Campari.
Pinkish negroni is made with pink wine (instead of gin).
A raultini is a variation using Aperol instead of Campari, giving its distinctive orange color, lighter alcohol content, and a bit of sweetness.
The most basic variation is served straight up in a martini glass with a splash of carbonated water floating on top of the alcohol mixture and a twist of lemon zest replacing the orange peel, known as the American version.
Other Italian versions substitute spumante brut or vodka for gin. A sparkling negroni is made with champagne or prosecco.

French 75

For ➊ cocktail
6 cl London dry gin or cognac or brandy
1 ts superfine sugar or 1.5 cl simple syrup
1.5 cl lemon juice
15 cl brut champagne or a good sparkling wine

Fill ½ a chilled shaker with cracked ice. Shake well. Then strain into a Collins glass half-full of cracked ice and top off with champagne.

Named after the 75-millimeter M1897, a light gun with a vicious rate of fire, the mainstay of the French field artillery in World War I. The drink was created in 1915 at the New York Bar in Paris, later Harry's New York Bar, by barman Harry MacElhone. The French 75, or Soixante-quinze was popularized in America at the Stork Club in New York.
(Some stories claim it was invented for the fighter pilots of the Lafayette Escadrille, made up of French and American aces. The story goes that they began toasting their fallen comrades with champagne but soon started to fortify the drink with something more potent. Lacking whiskey, the Americans opted for the more readily accessible Cognac. Others argue the drink was instead invented by the British who during World War I received a daily gin ration and began adding it to the locally available Champagne. This gin version is the recipe that first appeared in print, and is the best known French 75 recipe.)
The version with cognac with brandy or cognac yields a King's Peg, although often recipes for these omit the lemon and sugar.
You can use a champagne flute for esthetics.
Drawing by Jacques Tardi in 'Putain de guerre'.

Blackberry gin fizz

For ➋
50 g fresh blackberries
2 tbs sugar
12 cl gin
6 cl lime juice (from 2 juicy limes)
club soda
2 sprigs sweet basil or 2 thin lime wedges (for garnish)

Purée blackberries and sugar in a blender until as liquefied as possible. Strain purée through a fine-mesh sieve or tea strainer into two tall or collins-style glasses; discard seeds in sieve. Divide gin and lime juice between glasses and stir to combine.

Add ice to glasses then top each with soda and a sprig of basil or wedge of lime.