In my decades of playing horn (and dabbling in trumpet and trombone), I've been a voracious explorer of different approaches.
Many books have given me one or two nuggets.
Others have led me down not-so-helpful paths (Farkas "Art of Horn Playing" gave me a lot of good stuff in high school, but also indoctrinated me into flat chin static embouchure misery for many years)
Methods that I would genuinely recommend (in no particular order) at this stage in my journey, are as follows.
Richard Deane's "The Efficient Approach" is a masterful and modern book of wisdom about horn playing. He provides a lot of ideas that helped me, as well as a very well-rounded warmup.
You can purchase the book here, or read a longer review at Horn Matters.
The utterly inimitable Julie Landsman, former principal horn of Metropolitan Opera, created an amazing video series along with sheet music and a practice calendar, for her interpretation of the Caruso Method.
I studied this with Julie and have found great benefit from practicing these exercises. Listening to her talk through and demonstrate the exercises is far more rich than reading from a book.
Access Julie's full Caruso curriculum here
Malte Burba is an absolutely masterful performer and pedagogue, and I believe he truly understands how to create an easy, powerful, joyful, reliable approach to the instrument.
When I read his book I had a bunch of lightbulb moments and also a bunch of "GAHHH I KNEW THIS WAS TRUE HOW COME NOBODY ELSE SAYS THIS".
Check out a summary of his method here and purchase his Brass Masterclass here.
I may be biased... ok I'm definitely biased.
But I am incredibly proud of the method that I put together for brass players to truly understand and master not just the high range, but their practice habits, mindset, relaxation, and musical integration.
I don't know any other brass methods that talk about the role of emotion and mindset in results, but it's a HUGE component of what happens when we pick up the instrument.
If you want more info about high range magic, just visit this site and get a free 60 min high range masterclass.
I would not feel complete if I did not recommend this Arnold Jacobs wisdom compendium!
Arnold Jacob's legacy of teaching and thought-leadership was a huge contribution to the brass world.
If you have not purchased and read his book, I strongly recommend it.
Though it's not a "method book" per se, it has little nuggets of wisdom and is readable in small chunks. For years I would spend 2 minutes per day reading this as part of my practice routine. Always worth it.
The OG place to buy it is Windsong Press which has lots of great breathing devices and such too (stock up!). Or you can get it on Amazon.