  This is the second of a series of papers which are devoted to a comprehensive
theory of maps between orbifolds. In this paper, we develop a basic machinery
for studying homotopy classes of such maps. It contains two parts: (1) the
construction of a set of algebraic invariants -- the homotopy groups, and (2)
an analog of CW-complex theory. As a corollary of this machinery, the classical
Whitehead theorem which asserts that a weak homotopy equivalence is a homotopy
equivalence is extended to the orbifold category.
