Mint Leaves

Mints are aromatic, perrineal herbs that grow in Europe, Asia, Africa and America and since natural hybridisation of different Mint ( Mentha ) species are common, there are many hybrids and cultivars across the planet. Along with the mint, peppermint, spearmint and cornmint are known cultivars used regularly in condiments, foods and drinks. The fresh or dried mint leaf is the source of the mint flavour and aroma and is known to have several health benefits and has been used traditionally as a medicine for stomach ache, chest pain and headache, heartburn and diarrhea too. In drink making mint leaves or mint sprig is used as a garnish and is intended to provide that cool, menthol note to the nose, with spearmint being the most common mint in use a garnish.

Angostura Bitters Or To Taste

Angostura Bitters is a concentrated bitters based on gentian, herbs and spices, from the House of Angostura in Trinadad and Tobago. Note that the Angostura Bitters from the House of Angostura do not contain Angostura bark.
However, Angostura Bitters or Angobitter offered by other brands like Riemerschmid and Hemmeler, contain angostura bark, possibly to justify using the word "Angostura" in their names.

Lime Juice

Lime Juice being rich in Vitamin C is an excellent remedy for sore throat and aids in digestion and controls blood sugar, and also promoted weight loss. It is used for various culinary and non-culinary purposes all over the world. Lime juice is known to reduce or even reverse the effects of excessive alcohol consumption and intoxication.
The difference between Lime Juice and Lemon Juice is that although the sweet and sour Lemon and the bitter and sour Lime are two different fruits, they have similar properties and tastes similar too, the Lime, unlike the sweet and large Lemon, is used raw and is usually plucked green and has more bitterness and sourness in it's taste, and is grown better in tropical and sub-tropical climates.
In drink mixing, fresh lemon juice brings a tangy zing to so many classic drinks and in fact, it's the most used ingredient in drink mixing other than the liquors of course.

Sugar

Brown Sugar is a sucrose sugar with a distinctive brown colour from the presence of molasses, it is a partially refined or unrefined sugar containing sugar crystals and residual molasses giving it a distinctive taste and flavour of crystallised molasses or toffee. The taste of dark brown sugar is described as a caramel taste with a deep molasses flavour.
Brown sugar is used in cocktails where a caramel candy or toffee flavour is expected.

Caster Sugar is finely ground granulated sugar. It is not as fine a powdered confectioners' sugar and has a little grit to it. It is somewhere between confectioners' sugar and granulated sugar, and melts in mouth with a mild spicy feel to the tongue

Vanilla Sugar is the regular granulated sugar infused with vanilla flavour, by using vanilla pods and seeds to flavour the sugar. A home made alternative is to use vanilla sticks or pods in a jar of sugar and leave it sealed for 4 weeks to allow the vanilla flavour to infuse. Or to use granulated sugar and vanilla extract and blend in a mixer, although this ends up in powdered sugar.

White Rum

In the making of Rum, the produce of the fermentation and distillation process of molasses is a transparent spirit, which is then aged in vats or barrels and the end result of the ageing is Rum.

White Rum differs from Dark Rum in this process of ageing, while to produce a Dark Rum, the distillate is aged in a large charred oak barrel, White Rum is aged in big stainless still barrels.

There are no legal categorisatoin of Rums and it's just a matter of practice that dark rum is used in cooking or is drunk straight or with a Cola , white rums are mostly used in cocktails.

Tonic Water

Tonic Water originated in India when quinine was recommended to British officials and soldiers as a prophylactic against Malaria, quinine was mixed with soda to make it palatable, and since the British soldiers already received a ration of Gin, Gin and Tonic was born when Tonic Water was mixed with Gin and some sugar to make the medicine enjoyable.
Modern commercial tonic water produced for causal mixing in cocktails contains very little quinine and has citrus flavour additions and additional sugar or corn syrup for a better taste.