An exposure apparatus for performing exposure of a substrate to light via a reticle. The apparatus includes a first stage configured to hold a chuck. The chuck has a support base with an electrode, and forms a container, for one of the substrate and the reticle, together with a cover. The container electrostatically chucks the one on the support base by the electrode. A transporter transports the container in which the one is contained, and loads the chuck, which chucks the one, on the first stage without the cover. A second stage holds the other of the substrate and the reticle. The apparatus obtains a first positional shift amount between the chuck and the one chucked on the chuck before the transportation by the transporter, to measure a second positional shift amount between a reference mark on the chuck held by the first stage and a reference mark on the second stage, and corrects positions of the first and second stages based on the first and second positional shift amounts, to perform the exposure.