  The paper applies the JSJ decomposition and Koda-Ozawa's annulus
classification to analyze the annulus configuration in a handlebody-knot
exterior. We introduce the notion of the annulus diagram, to pack the
configuration into a labeled graph, and classify genus two handlebody-knots in
terms of their annulus diagrams. Applications to handlebody-knot symmetries are
discussed; methods to produce handlebody-knots with various types of annulus
diagrams are also presented.
