From a viewpoint of transport properties, topological insulators are the materials that are insulating in the bulk but are metallic at their edge. After briefly introducing the basic phenomena such as Dirac fermions and quantum spin Hall effect for topological insulators, we describe the details of the quantum oscillations originating from the surface state of a three-dimensional topological insulator Bi_1-xSb_x, which was observed for the first time by our group. Intriguingly, this material was found to exhibit a novel angular-dependent magnetoresistance oscillation phenomenon, whose origin is still unknown but probably reflects a new physics in the surface transport properties of the topological insulator.