Quasicrystals and particularly crystal-quasicrystal interfaces are fascinating surface scientists for more than two decades due to the several unexpected phenomena that occur at the conjunction of incompatible, but nevertheless related structural properties. In this project, the oxidation at high temperature of the fivefold-symmetry surface of an icosahedral Al70Pd20M10 quasicrystal was principally investigtated. The formation of a 5 A thin well-ordered aluminum-oxide film represents a complete new kind of crystal-quasicrystal interface. The stoichiometry of the near-surface region was investigated by means of Auger electron spectroscopy and x-ray photoelectron spectroscopy and both confirmed the oxidation of only the Al atoms of the quasicrystalline substrate. The patterns obtained by means of low-energy electron diffraction from the aluminum-oxide share several similarities with those obtained from the oxidation at high temperature of NiAl(110) faces. This intermetallic alloy posses the CsCl structure, which has a strong relationship with the icosahedral structure. The (110) face is then the "qanalogue" of the pentagonal surface of an icosahedral quasicrystal. The affinity of the two structures is illustrated by the CsCl-like AlPd domains observed, by means of secondary-electron imaging, after Ar+-sputtering of the quasicrystalline surface [1]. The aluminum-oxide film consists, as in case of NiAl(110), of pairs of ?-Al2O3-like domains [2]. Due to the fivefold symmetry of the quasicrystalline surface, five pairs of these domains rotated by 72Awith respect to each other are observed in our case. Each pair is aligned along one of the five twofold-symmetry directions present in the fivefold-symmetry surface and is a consequence of the strong affinity of the icosahedral structure for the CsCl structure. In the diffraction patterns, spots arising from the quasiperiodic substrate are after the oxidation process still present, pointing out that the quasicrystalline order is not disturbed by the oxidation process. The average in-plane size of the aluminum-oxide domains was evaluated to be approximately 35 A Oxide thin films are important supports for dispersed metal catalysts and magnetoelectronic devices. In the former, for instance, a catalytically active component such as a transition metal is dispersed over a suitable support material, usually an oxide like alumina or silica. Aluminum-oxide films are, because of their electronic characteristics and their remarkable flatness, also widely used as substrate for semiconductor epitaxy. PbTe and CdTe are two important binary semiconductors. The former is IV-VI narrow band-gap semiconductor used in infrared detectors, while the latter, a II-VI semiconductor exhibiting a wide-band gap, is one of the most important material in the photovoltaic cells research field. In this project, we used the oxidized fivefold-symmetry surface of i-AlPdMn as substrate for the deposition of PbTe and CdTe. Diffraction patterns obtained from thin films of both materials exhibit, instead of the usual spots, diffraction rings. They are characteristics of nanocrystallites having a random azimuthal orientations but a well-defined polar orientation; the (001) face and the (111) face in case of PbTe and CdTe, respectively. From the diffraction patterns, average domain sizes of 35 A were deduced, which corresponds to the average size of the aluminum-oxide domains. We argued that, in contrast to normal epitaxy where the domain size of the deposited material is given by the lattice mismatch between the growing film and the substrate, it is here given by the size of the substrate. This was confirmed by the results obtained from the deposition of Al onto the same substrate. Face-centered-cubic Al(111) domains with a similar average size are observed in this case. Angle-resolved photoemission spectroscopy investigations on the PbTe films were performed. No significant confinement effects could be observed. Because the samples have been exposed to air, in order to transfer them to the measurement chamber, we argue that oxygen has changed the electrical properties of the films, preventing us to observe any size effect. We also performed angle-resolved photoemission spectroscopy measurements on Ag films deposited onto the fivefold-symmetry surface of icosahedral AlPdMn and onto the tenfold-symmetry surface of decagonal AlCoNi as model for confinement effects occurring due to the incompatible symmetries between the crystalline films and the quasicrystalline surfaces. Ag, in a face-centered-cubic structure, exhibit in both cases its (111) face parallel to the substrates surface. By analyzing the Ag sp-derived quantum-well states, we assert that the interface with the quasiperiodic material constitutes an efficient barrier for electron propagation, due to lack of common point-group symmetries between Bloch-like and critical wave functions. Finally, the depositions of Si and Ge onto the fivefold-symmetry surface of icosahedral AlPdMn were investigated. Low-energy electron diffraction and secondary-electron imaging investigations lead to the conclusion that both materials have a three-dimensional amorphous growth mode for a large substrate temperature range. This is, probably, a consequence of the high directionality of the atomic bonds in these semiconductor materials. At temperature above 370 K, Auger electron spectroscopy measurements show that Si noticeably diffuses into the substrate, which prevents a probable crystalline growth mode at high temperature.