My characters frequently end up at Balls or informal dances, and I love to include the glittering atmosphere of the ballroom, or Almacks Club, where there is lots of occasion for romance, scandal, and intrigue. And in every modern woman (and in quite a few modern men) there is the sense of the glamour of those old stately dances, and a perhaps a desire to experience it nowadays (hence the tourist market in Jane Austen functions, which I always think would be a lot of fun. )
There is a fabulous blog post here describing the influence of Almacks especially: https://janeaustensworld.wordpress.com/tag/lady-jersey/
Some of the dance names do not always feature in our lives these days, like the Quadrille but how on earth did it look? There is the famous drawing of Lady Jersey introducing the Quadrille, of course:
... thus we see some of the elegant and risque steps! But here is a recreation of the dance so that we can see it in action:
La boulangère was a French dance regularly danced in London ballrooms, and I found this delightful expression of it, the dancers in the costume of the Revolutionary times:
We think we are familiar with the Waltz, our vision being perhaps on the later Struass waltzes and the energetic performances we see in films. Or perhaps the more elegant Fred Astaire numbers, but the waltz of Regency times looked very different.
Another example even had a group part to the waltz. But mostly the waltz was a couples dance, and allowed a man and a woman to be in shocking proximity and also offered them the best opportunity to further relations by talking. You can understand why the waltz causes a sensation and a scandal. It was banned from many ballrooms at first, then the high born patronesses of Almacks Club, ladies who were the most fashionable and richest in town, and the highest sticklers of respectability to boot, sanctioned it within their portals. These leaders of fashion permitted the dance (which was, of course great fun), but a young lady in her first season had to be presented to a suitable partner by the patronesses before she was able to waltz at any other party! Doing the waltz before permitted made a girl "fast"!
One should not be not be too romantic about the waltz, though. No doubt many girls had to be closer than they wished to to leering gentleman, or perhaps one who had just have eaten onions!