Reddit mentions of The Triangle of the Scene: A simple, practical, powerful method for approaching improvisation

Look to the right of your screen and down a little bit.

Based on your recent post, I feel like you're looking for a training program in book form. The UCB Manual is the most comprehensive and closest thing to that, but take it all with a grain of salt as at a certain point it does start teaching the UCB style. Novices may take some things to mean these are this-is-the-only-way-to-do-things hard and fast rules, but it's just the way to play their aesthetic. Be open to other possibilities.

Some books, like the recent Will Hines book or Napier's Improvise, are very good but I recommend them after you've done a bit of improv. Same with this, this, and this.

Johnstone's Impro is great for a peek into story-based
British style improv. His passages on status are invaluable.

I personally don't care for Huack's Long-Form Improv, mostly because at the beginning of the book he tries to distill all improv comedy down into an equation, which is way too simplified for my tastes. Improv Wins is a decent, breezy book, but I don't like how they pose scenario questions and then suggest that there is a "correct" response you should make. Still, if you can glean insight from a book, even an understanding of disagreement, then that makes the book valuable in some way.

The only real way to learn improv is to do it and not be afraid to make mistakes and missteps along the way. You will not get improv right the first time.

The Triangle of the Scene: A simple, practical, powerful method for approaching improvisation by Paul Vaillancourt