  We develop an obstruction theory for homotopy of homomorphisms f,g : M -> N
between minimal differential graded algebras. We assume that M = Lambda V has
an obstruction decomposition given by V = V_0 oplus V_1 and that f and g are
homotopic on Lambda V_0. An obstruction is then obtained as a vector space
homomorphism V_1 -> H^*(N). We investigate the relationship between the
condition that f and g are homotopic and the condition that the obstruction is
zero. The obstruction theory is then applied to study the set of homotopy
classes [M, N]. This enables us to give a fairly complete answer to a
conjecture of Copeland-Shar on the size of the homotopy set [A,B] when A and B
are rational spaces. In addition, we give examples of minimal algebras (and
hence of rational spaces) that have few homotopy classes of self-maps.
