The Thesis is devoted to the theoretical and numerical study of the enhancement ofrnthe local electric field and the induced optical bistability (IOB) in metal ellipsoidalrnand spherical dielectric nanoparticles covered by a metal shell with nonlinear dielectricrnfunctions. In the electrostatic approximation, specification of the IOB domain reducesrnto an analysis of the algebraic cubic equation for the local electric field in the particlernas a function of the external electric field. The comparatively simple analysis ofrnroots of a cubic equation, proposed in the Thesis, allowed us to find the range ofrnthe amplitudes of incident electromagnetic wave and their frequencies where the IOBrnexists and study its dependence on the parameters of the problem. The results ofrnnumerical computations for metal and metal covered semiconductor nanoparticles arernpresented graphically.rnIt is shown that the local field in metal spherical particles with dielectric core inrnan external varying electric field has two maxima at two different frequencies. Thernsecond maximum becomes more important with increment in the metal fraction. Duernto the nonlinear dielectric function of the core, the composite of these inclusions mayrnhave two optically induced bistability domains at different frequencies. At rather highrnmetal fraction, two bistability domains merge and form one entire bistability domain.rnThe parameters of these domains are studied numerically. In the Thesis we focusesrnon the second bistability domain. This domain exists in a comparatively narrowrnfrequency range and its onset fields are lower than those of the first bistability domain.rnThe lowest bistability onset fields are obtained in the entire domain. This peculiarityrnof the optical induced bistability in the metal composite with small dielectric coresrncan be attractive for possible applications.rnIn the Thesis it is shown that the enhancement factor of the local electric field inrnmetal spherical or cylindrical nanopacticles with dielectric cores imbedded in a dielectricrnmatrix have two maxima on two resonant frequencies. The second maxima forrnxvrnxvirnthe inclusions with large dielectric cores covered by a thin metal shell is comparativelyrnsmall. With increasing in a metal fraction in the inclusion, both enhancement factorsrngrow. For large metal fractions, the maxima of the enhancement factors become thernsame order of magnitude and considerably large. At a special relation between therndielectric constants of the core and the host matrix, the two maxima merge and showrnfurther increment. The numeric calculations show that the real and imagine parts ofrnthe refractive index of the composites of metal inclusions having â€small†dielectricrncores have new interesting features.rnThe optical properties of metal/dielectric composites (metal with dielectric corernand pure metal inclusions) in passive and active host matrices are studied. It is shownrnthat the real and imaginary parts of the refractive index of the composites with metalrncovered inclusions have two maxima at two resonant frequencies. Both types of therncomposite show a strong anomalous dispersion of the real part of refractive index.rnThe active host matrices can considerably reduce the absorption and provide thernconditions for propagation of weakly damping electromagnetic waves on the resonantrnfrequencies. The weakly spreading wave packets of light of a negative group velocityrncan be experimentally observed in these composites