Core Book, or Method Book

A core, or method book, is a book used by piano or keyboard students in their lessons with a teacher. It typically introduces the specific concepts and important ideas being taught in the lessons, in a logical learning sequence.

A core book is different from a repertoire book, which contains only pieces of music for the student to play. Repertoire books may contain a small amount of explanations, definitions, and perhaps composers' biographies, but they contain mostly pieces. 

On the other hand, a core book's main purpose is to present materials; the pieces in each chapter usually illustrate or use the specific concepts being taught in that chapter.

It is important to note that method books designed for use with young students are different from method books designed for adult students, because there are differences in the way children and adults learn.