（ABSTRACT）

After an overview of several brane models, we present the effective equations to describe the four-dimensional gravity of a brane world, assuming that gravity is confined on the $Z_2$ symmetric brane. Applying this formalism to the Randall-Sundrum brane world model, we find two new additional terms in the Einstein equations: One is the quadratic term of the energy-momentum tensor of matter field and the other is the 5-dimensional Weyl curvature term. Although the four-dimensional effective equations are not closed and further information from the bulk is required, those terms may provide us windows to search for the extra dimensions. We then discuss about some effects of those terms on cosmology and compact objects. Using the similar formalism, we also analyze other brane models; the model with a bulk dilaton field motivated by Ho\v{r}ava-Witten model, and the induced gravity brane model proposed by Dvali, Gabadadze and Porrati. In the latter case, we find that an effective cosmological constant on the brane can be extremely reduced in contrast to the case of the Randall-Sundrum model even if a bulk cosmological constant and a brane tension are not fine-tuned.