One of the really interesting things the Madrusans have done with their Cocktail Companion is to formally deploy a modern drink typology that reuses, extends, and augments historical drink categories that were mostly forgotten in the 20th century to make them more relevant, today, particularly in their style of bars.
Collins: spirit + lemon juice + sugar + soda
Subsumes the Coolers. A popular and expanded drink form in the Petraske diaspora. (Notably, in their hands, these drinks tend to not be large scale thirst quenchers, rather a kind of iced fizz, sans egg white, with high flavor concentration.)
Rickey: spirit + lime juice + sugar + soda
What was one drink is now a home for Collinses and Coolers made with lime juice.
Buck & Mule: spirit + citrus + ginger syrup + soda
The buck didn’t even really qualify as a category, historically, and the mule was a lone drink, but given the fondness for ginger syrup in the Petraske diaspora, they now have a large repertoire to document.
Highball & Mixed Drink: spirit/wine + soda/carbonated mixer/juice
I feel their pain—these drinks gotta go somewhere. Stuff like the Bloody Mary winds up here.
Cup & Punch: spirit(s) and/or wine, liqueur(s) + citrus juice + sugar + spices + (optional water)
Reflects that contemporary punch is beloved by the cognoscenti, but far removed from its original megacategory status. Even Further diminished, as many punches are carved out of this to their own, separate “Tropical” category (below)
Fizz: spirit + lemon + sugar + egg white + soda
Refocused category that, again, reflects the Petraske school’s undying devotion to the egg white drink (for which I am most grateful).
Sour: spirit + citrus juice (predominantly lemon) + sugar + (optional) egg white
Fairly obvious, although the Daiquiri and its variations have been spun off into their own category (below).
Crusta, Daisy & Sidecar: spirit + citrus juice + liqueur(s) and/or syrup(s)
I’m still not totally sold on “crusta” as a catchall for any daisy-ish drink with a sugared rim, nor that the Sidecar is a clear drink category (they uncomfortably treat it as halfway between a category and break-out like Daiquiri or Negroni). Sort of begs the question: if the only difference, today, between a sour and a daisy is whether there’s a liqueur or flavored syrup in it, why does the distinction even matter?
Gimlet & Shake: spirit + lime juice + sugar
I apparently don’t run in the right circles to be familiar with the “Shake”, but the Gimlets seem to all be gin drinks, and the same rough idea with other spirits is a “Shake”. The only commonality seems to be sweetened lime juice and/or lime cordial, so this is sort of like the expansion of the Rickey (above). The drinks could otherwise be Sours or Daisies, so it’s a little awkward. But still kind of interesting.
Daiquiri: rum + lime + sugar
Drink to category. They have a lot of drinks to discuss, here, but they’re mostly a mix of sours and daisies, so I’m not sure how I feel about it.
Batida: spirit + lime chunks + sugar
Actually a rough template for an umbrella of “rustic” drinks that typically involve muddled or shaken fruit pieces and such. This needed to happen. It’s nothing new “south of the border”. It’s one of the smallest recipe sections of the book, and it could probably be much longer.
Fix & Swizzle: spirit + citrus juice + sugar and/or liqueur and/or syrup
The key detail omitted in the formula is that these are all crushed ice drinks. This all makes total sense for these recipes and how they are typically deployed. Again, Petraske school obsessions are showing through, here, and I generally love it.
Cobbler: wine, fortified wine and/or spirit + sugar and/or liqueur + (usually) citrus juice
Another crushed ice drink category that pairs with the above. Nobody has done more for the modern cobbler than the Petraske diaspora. 
Julep: spirit + sugar + mint
Smash: spirit + sugar + mint + muddled fruit
Stinger: spirit + creme de menthe
The Madrusans lump these together, despite offering different templates, because they are minty. At least the Juleps and Smashes have a lot of structural commonality, including crushed/cracked ice. I’m not sold on the Stinger and its friends being tacked on, but if not here, where?
Negroni: gin + sweet vermouth + Campari
Drink to category. There are now a lot of them, they have to go somewhere, and it is commonplace to describe them all as “negronis”.
Martini: gin/vodka/genever/pisco/some agave/sherry/sake + vermouth + bitters
Long a de facto category of Martini-related drinks that briefly (1980-90s) expanded to encompass every drink before contracting again. As a practical matter, I am okay with it, but the genever drinks would belong in the Manhattan section (below)
Manhattan: whisky/brandy/some agave + vermouth + bitters
Separating these from the Martinis can get a little arbitrary, but there are a lot of drinks to deal with, and most are intuitive.
Old Fashioned & Sazerac: spirit + sugar + bitters
The closest we get to a “cocktail” category, and it is deep. Again, nobody has done more for the Old Fashioned than the Petraske diaspora.
One of the Petraske peculiarities, however, is that there’s no place for, say, a Whiskey Cocktail served up—it’s always built in a rocks glass and iced.
Flip: spirit + whole egg or egg yolk + sugar
An easy one. Maybe the easiest?
Toddy: spirit + sugar (predominantly honey) + boiling water
A small section of obvious cases.
This winds up the Madrusan’s primary “branches” as they call them. There is no “Cocktail” group. No slings. No sangarees. No pousse-cafés (okay by me).
They then proceed with some bonus sections that avoid lumping a ton of recipes under “Mixed Drinks” but are probably only satisfying if you approach them from just the right angle:
Aperitivo & Spritz
Sparkling
Beer
Tropical
Coffee
Cream
Non-Alcoholic