Isolation and characterization of mechanically exfoliated black phosphorus flakes with a thickness down to two single-layers is presented. A modification of the mechanical exfoliation method, which provides higher yield of atomically thin flakes than conventional mechanical exfoliation, has been developed. We present general guidelines to determine the number of layers using optical microscopy, Raman spectroscopy and transmission electron microscopy (TEM) in a fast and reliable way. Moreover, we demonstrate that the exfoliated flakes are highly crystalline and that they are stable even in free-standing form through Raman spectroscopy and TEM measurements. A strong thickness dependence of the band structure is found by density functional theory (DFT) calculations. The exciton binding energy, within an effective mass approximation, is also calculated for different number of layers. Our computational results for the optical gap are consistent with preliminary photoluminescence results on thin flakes. Finally, we study the environmental stability of black phosphorus flakes finding that the flakes are very hydrophilic and that long term exposure to air moisture etches black phosphorus away. Nonetheless, we demonstrate that the aging of the flakes is slow enough to allow fabrication of field-effect transistors with strong ambipolar behavior. DFT calculations also give us insight into the water-induced changes of the structural and electronic properties of black phosphorus.@en