It's called an epigraph.
The quote at the beginning of a chapter is typically called an "epigraph." It is a quotation or excerpt that sets the tone or theme for the content that follows in the chapter.
Heading
A heading.
at the beginning of the book, or at the beginning of each chapter
Nothing makes us so lonely than our own secrets.
It is called an epigraph (see http://en.wikipedia.org/wiki/Epigraph_(literature) ).
There are many elements that could appear, although not all elements appear in all books. These include things like a copyright page, a title page, a dedication page, a foreword, and a table of contents.
The first chapter in the book "Flipped" by Wendelin Van Draanen is called "The Very Beginning."
Those are called "illustrations." They can be found at the beginning of a book or chapter to provide visual context for the text.
At the beginning of chapter 5, it is Monday morning.
At the beginning of a chapter
December!!!
The beginning chapter of "Moby Dick" is set in December.
This quote is on page 270, chapter 25 "Finding Ruthie"
end of chapter 18 and beginning of chapter 19