Special classes of closed four-manifolds

We present several results and state some open problems on the classification of topological and geometric structures of closed connected oriented (smooth) four-manifolds. In particular, we discuss many interesting classes of closed four-manifolds satisfying additional properties, that is, spin manifolds, manifolds with special homology (resp. homotopy), exact manifolds, geometric manifolds, and smooth manifolds. The results are obtained by using methods and techniques from algebraic and differential topology, and homological algebra.