The　band　structure,　density　of　states,　optical　properties,　carrier　mobility,　and　loss　function　of　graphene,　black　phosphorus　(BP),　and　molybdenum　disulfide　(MoS2)　were　investigated　by　the　first-principles　method　with　the　generalized-gradient　approximation.　The　graphene　was　a　zero-band-gap　semiconductor.　The　band　gaps　of　BP　and　MoS2　were　strongly　dependent　on　the　number　of　layers.　The　relationships　between　layers　and　band　gap　were　built　to　predict　the　band　gap　of　few-layer　BP　and　MoS2.　The　absorption　showed　an　explicit　anisotropy　for　light　polarized　in　(1　0　0)　and　(0　0　1)　directions　of　graphene,　BP,　and　MoS2.　This　behavior　may　be　readily　detected　in　spectroscopic　measurements　and　exploited　for　optoelectronic　applications.　Moreover,　graphene　(5.27　x　10(4)　cm(2).V-1.　s(-1)),　BP　(1.5　x　10(4)　cm(2).V-1.　s(-1)),　and　MoS2　(2.57　x　10(2　)cm(2)　.V-1.s(-1))　have　high　carrier　mobility.　These　results　show　that　graphene,　BP,　and　Mos(2)　are　promising　candidates　for　future　electronic　applications.