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The electronic structure of interfaces between LaAlO$_3$ and SrTiO$_3$ isstudied using local spin density approximation (LSDA) with intra-atomic Coulombrepulsion (LSDA+U). We find that the nature of the interface metallic states isstrongly affected by the type of the structure (sandwich or bilayer) and by thetermination surface of LaAlO$_3$. In all structures the atomic relaxation playsa crucial role in the electronic properties of the system. While in sandwichesthe structural relaxation produces a significant polarization in SrTiO$_3$ andJahn-Teller like splitting of Ti $3d_{xy}$ orbitals, in AlO$_2$-terminatedbilayers the relaxation occurs primarily in LaAlO$_3$ and results in aninsulator-metal transition which has been observed experimentally withincreasing thickness of the LaAlO$_3$ layer.

Structural relaxation and metal-insulator transition at the interface between SrTiO3 and LaAlO3