I will present an introduction to flat and almost flat manifolds. Then I will define a spin-structure on such objects and finally I will prove the following: Let M be any almost-flat oriented 4-manifold different from the torus with intersection form Q_{M}. Then Q_{M} = 0 if the first Betti number b_1(M) = 1, Q_{M} = H if b_1(M) = 2 and Q_{M} = 2H if b_1(M) = 3. Here H is the hyperbolic form with intersection matrix [0,1 1,0] of rank 2.