The quantum size effects (QSE) make it possible to control the dimensions of self-assembled nanostructures. An important goal in present day surface science is to grow uniform sized self-assembled nanostructures. One system which has displayed a number of interesting surface structures is Pb/In grown on a Si(111) substrate. The first part of the thesis discussed Pb islands grown on the anisotropic Si(111)-In(4x1) substrate. In addition to a preferred height of 4 monolayers due to QSE, these islands grow as nanowires with a preferred width of 660nm due to strain driven growth from the anisotropic substrate. Islands grown on the In(4x1) substrate also retain their preferred height to room temperature in contrast to previously observed critical temperatures of 250 K or less for islands grown on other substrates. Then In islands were grown on Si(111)-Pb-alpha-sqrt3 x sqrt3 substrate. The In islands in face-centered cubic (FCC) structure were found to have a preferred height of 4 monolayers due to QSE. With further depositions, an FCC to body-centered tetragonal(BCT) structure transition is observed. The In bct islands was found to have unexpected fast growth rate compared to FCC structure, which indicate the extra high mobility of In atoms. In the last part In islands were grown on varies of In phases at low temperature. Conversion between submonolayer In phases are observed. Due to the highly mobility of In atoms, the QSE effects observed on the Pb alpha phase is not observed.