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The enhancement of electronic and optical properties of semiconductor nanostructures is known as a direct consequence of the spatial confinement of carriers. However, the physics of quantum confinement is still not entirely understood. This work focuses on a qualitative study of quasi-zero dimensional II-VI semiconductor nanostructures (quantum dots QDs). In particular, commercially available as-received and heat treated CdSxSe1-x QDs embedded in a dielectric matrix were investigated by means of linear and nonlinear spectroscopy techniques. Low wavenumber Raman in off-resonance scattering regime was applied in order to obtain key-properties of the nanocrystals, such as the QD's size and the distribution of the QD's size inside the inhomogeneous broadening. Moreover, by careful selection of the polarization geometries, different acoustic vibrational modes could be evidenced. In comparison to the bulk, 3D confinement of carriers leads to modifications in the energy distribution in a QD and as a consequence, the intensity of the acoustical phonons is enhanced. However, only 2 acoustic vibrational modes (labelled l=0 and l=2) are Raman-active, which were selectively excited using linear polarized laser light in parallel- and cross-polarized excitation geometries. The QD's size was determined using the dependence of the frequency of the acoustic vibrational mode on the diameter of the vibrating particle, whereas the QD's size distribution was estimated from the normalized full width at the half of the maximum (FWHM) of the symmetric acoustic vibrational mode. In order to study relaxation mechanisms, which in quantum confined systems occur on a ps time scale, ultrafast spectroscopy techniques using laser pulses in the fs range must be employed. To this purpose, fs-FWM and fs-PPT measurements were performed on CdS0.6Se0.4 QDs of 9.1 nm in diameter, embedded in a glass matrix. The laser pulses employed in these experiments were circularly polarized, careful selection of the polarization geometries making different nonlinear processes available to study. It was shown that the relaxation of polarization selection rules depend strongly on the symmetry of the nanocrystals under discussion. The investigated nanocrystals belong to the symmetry group C2v or lower and their hexagonal crystal shape could be evidenced. The relaxation of selection rules was explained in the framework of the 4-level system, including a ground state, two exciton states and a biexcitons state. The appearance of FWM and PPT signals in forbidden polarization geometries was shown to be due to exciton state splitting due to lowering of the QD’s symmetry and due to the strong Coulomb interaction between carriers belonging to the same nanocrystal. Moreover, the significant difference in the origin of the gratings created by two pulses having the same and opposite polarizations, respectively. The intensity of the FWM signals should be the square of the intensity of the PPT signals and therefore the PPT measurements were employed as a check method for the results yielded by the FWM technique. The efficiency of circularly polarized femtosecond FWM spectroscopy techniques was proved once more in the investigation of heat treated CdSe QDs embedded in a dielectric matrix. The role of non-phonon energy relaxation mechanisms in the exciton ground and excited state of the QDs ensemble was extensively studied. Moreover, the dependence of the crystal shape asymmetry on the particle size and on the growth conditions could be estimated. It was shown, that the most efficient procedure to grow high quality nanocrystals is a longer heat treating at lower temperatures. In this case, the particles have more time to "nucleate" and to adopt a more "symmetric" shape. Further, the relaxation of excitons was extensively investigated. It was shown, that the electron intraband dynamics depend strongly on the Coulomb interaction between electrons and holes. Even at low excitation density, the Auger processes cannot be ignored. Auger autoionization of excitons followed by capture of carriers in surface states and deep traps in the dielectric matrix slow down the exciton relaxation process leading to an exciton lifetime ranging on a ps time scale. The relaxation of excitons from higher lying energy levels occurs also on two paths. At the beginning of the relaxation process (t31 < 400 fs), Auger-like thermalization of carriers is responsible for relaxation of the electron from 1pe into its 1se state, while the hole relaxes rapidly through its dense spectrum of states in the valence band. This process is immediately followed by capturing of carriers in deep traps, situated at the semiconductor-dielectric heterointerface. The traps are a consequence of the QD's asymmetry: the more and the deeper the traps, the higher the asymmetry of the nanocrystals (the band offset  is larger). This work presents a complete characterization of CdSSe QDs embedded in a glass matrix. The most important properties of the nanocrystals like QD's size and size distribution inside the inhomogeneous broadening were determined by means of low wavenumber Raman spectroscopy. In order to draw a full picture of these nanoparticles further complementary nonlinear spectroscopy techniques were used. Invaluable conclusions were available as a result of TI-FWM techniques applied in the framework of transient grating on 3D confined nanocrystals embedded in a glass matrix. The polarized the TI-FWM measurements were successfully performed on different QDs ensembles in order to determine symmetry properties and to describe the ultrafast relaxation mechanisms. This work brings additional contribution concerning the preparation of high quality QDs by presenting the effect of different growth conditions on the QDs symmetry, thus indicating a way for efficient manufacturing of nanocrystals.