There are many wonderful music books available, including method, etude, and solo books. The list below includes several that I often use in lessons, but there are many great books not included here. I encourage more advanced students to discover new pieces on their own as well, and bring them to lessons.
Beginning Books
Rubank Elementary Method - French Horn in F or E-Flat and Mellophone
Student Instrumental Course Tunes for French Horn Technic: Level 1 by James D. Ployhar, Fred Weber
First Book of Practical Studies for French Horn by Robert Getchell
Tritons: 8 Easy Pieces for F/Eb Horn and Piano by Bram Wiggins. Hal Leonard
1st Recital Series for F Horn, published by Curnow/Hal Leonard
Canadian Brass Book of Beginning Horn Solos
Canadian Brass Book of Easy Horn Solos
The Greatest Solo Songbook – for Horn by Larry Clark. Arranged by Sandy Feldstein. Yamaha Advantage. Carl Fischer
The Really Easy Horn Book: Very first solos for horn in F with piano accompaniment. Gunning & Perason. Faber Music
Horn Solos: Book One by Arthur Campbell. Faber Music
Simple Studies for Beginner Brass: For trumpet and other treble clef brass by John Miller. Faber Music
The Really Big Student Songbook by Eric Bolvin (https://bolvinmusic.com/product/the-really-big-student-songbook/)
Classic Festival Solos (Horn in F), Volume 1, HORN BOOK (not accompaniment), Alfred Publishing
Classic Festival Solos (Horn in F), Volume 2, HORN BOOK (not accompaniment), Alfred Publishing
Easy Popular Movie Instrumental Solos. (Horn in F). Book & CD. Alfred Music Publishing
Rubank Intermediate Method - Horn (F, Eb Alto or Mellophone)
60 Selected Studies, By C. Kopprasch. For horn. Kalmus Edition. Studies and Technique. Published by Alfred Music Publishing (AP.K04527)
Concert and Contest Collections - French Horn (French Horn Solo Part)
Lots of film music books, such as Best of John Williams and music from movies and TV: Lord of the Rings, Star Wars series, Harry Potter, Disney Favorites, etc.
Master Solos Intermediate Level - Horn (Book/CD Pack). Edited by Linda Rutherford and Louis Stout, Sr.. Master Solos. Published by Hal Leonard (HL.841328). Louis Stout.
The Horn Collection: 14 Pieces By 11 Composers. Schirmer.
Eighteen Sacred and Spiritual Solos, by Daniel Kelley.
First Solos for the Horn Player, by Mason Jones.
Solos for the Horn Player, by Mason Jones.
Morceau De Concert - Horn/Piano, By Camille Saint-Saens (1835-1921). For F horn and piano. Belwin Edition. Classical Period. Difficulty: medium. Published by Alfred Music Publishing
Solo works by Gliere, Glazunov, and some movements of Mozart's Horn Concertos
Advanced Books
The Art of French Horn Playing, For horn. Brass - French Horn Method or Collection; Method/Instruction. Instructional book. Published by Alfred Music Publishing (AP.0021)
On Playing the Horn Well, by Froydis Ree Wekre
Progressive Studies in Flexibility and Range Development for French Horn, by Fred Teuber
60 Selected Studies, By C. Kopprasch. For horn. Kalmus Edition. Studies and Technique. Published by Alfred Music Publishing (AP.K04527)
Melodious Etudes for Trombone - Book 1, (Selected from the Vocalises of Marco Bordogni). By Joannes Rochut. For Trombone. Published by Carl Fischer
W.A. Mozart Horn Concertos, Schirmer or Barenreiter editions
ABRSM Grade 6-8: Principal Horn: 13 repertoire pieces and studies for Horn
Strauss Concerto No. 1, Op. 11
Beethoven Sonata for Horn and Piano
HORN Anthology, Boosey & Hawkes
Orchestral Excerpts for the Horn Player (Arthur Labar), Thompson Edition complete horn parts, Pottag excerpt books, IHS excerpts compiled by Darren Robbins.
Various etude books: Rubank Advanced book 1 & 2, Maxime-Alphonse books 1-6, Gallay, Mueller, Kling, Hackleman, etc.
Solo works by Bach, Dukas, Gliere, F. Strauss, Haydn, Telemann, etc…
Unaccompanied or fixed media works, by Krol, Ketting, Persichetti, Naigus, Malcolm Arnold, Dante Yenque, Paul Basler, etc.