(please ask us first which one we recommend for your specific situation)
For Young Beginners
John W. Schaum, Making Music At The Piano (all levels)
John W. Schaum, Fingerpower (all levels)
For Teenage Beginners
Wunderkeys for older beginners--pop tunes
For Adult Beginners
Alfred's Basic Adult Piano Course
Siskind, Jazz Piano Fundamentals
Beginner to Intermediate (in addition to method books)
Schirmer, Selected Piano Masterpieces - Early Intermediate Level
Schirmer, First Lessons in Bach
Palmer, The Complete Book of Scales, Chords, Arpeggios & Cadences
Intermediate to Advanced (just to get us started)
Schirmer, Sonatina Album
Bach, Inventions and Sonatinas
Anthology of Romantic Piano Music, Anthology of Impressionist Piano Music, Anthology of 20th Century Piano Music
Burgmüller, Czerny & Hanon -- Piano Studies Selected for Technique and Musicality
Hanon, The Virtuoso Pianist In Sixty Exercises For The Piano
Wunderkeys Pop Studies for Piano
Hisaishi, Ghibli Best Stories
(please ask us first which one we recommend for your specific situation)
For Beginners
Barbara Barber, Solos for Young Violinists (later volumes for Intermediate to Advanced)
Whistler, Introducing the Positions
Intermediate to Advanced (in addition to method books)
Barber, Scales for Young Violinists and Scales for Advanced Violinists
Franz Wohlfahrt, 40 Elementary Etudes for Violin, Op 54 and 60 Studies, Op. 45
Carl Flesch, Scale System for Violin
Learning Music
For kids and teens: NoteWorks (on Apple and Android) or on Kindle Fire
For adults and advanced learners: Tenuto
For all: Musictheory.net Theory Lessons and ABRSM Music Theory Trainer
Reading Music
ForScore for iPads
MobileSheets for Android Tablets
Understanding Music
Robert Hutchinson, Music Theory for the 21st-Century Classroom