In recent years, coinage metal nanoparticles have emerged as materials with largest quadratic optical nonlinearity. Their first hyperpolarizabilities (β) are very high (105-106 x 10-30 esu) but such large values were quite unexpected because of their apparently centrosymmetric bulk structure. Only a small second harmonic generation (SHG) from coinage metal nanoparticles is expected through higher order multipolar (e.g., quadrupolar) polarization mechanisms. Various possible reasons have been attributed to the observation of large β values in coinage metal nanoparticles. They are: 1) Particles may not be overall centrosymmetric (as appears from the TEM pictures) which, in turn, can make SHG electric dipole allowed, 2) Several polarization mechanisms (dipolar, quadrupolar, retardation, etc.) may be operating simultaneously to render SHG very efficient, 3) SHG can be resonance enhanced if the incident or SH photons fall within the surface plasmon resonance (SPR) absorption bands or higher energy interband transitions in the metal particles, and 4) Surface capping agents used for stabilization of the nanoparticles in solution alter the SH response. It is, therefore, important to experimentally find out which of the above mentioned possibilities are dominant and under what conditions we can identify the contribution of various mechanisms to the overall SHG response of the coinage metal nanoparticles. In this thesis work, the origin of SHG from copper (one of the coinage metals) nanoparticles has been investigated using hyper-Rayleigh scattering (HRS). In chapter 1, an introduction to metal nanoparticles and their optical properties have been presented. A general introduction to second order nonlinear optics and various methods for the determination of first hyperpolarizability are provided. A literature survey on the second order NLO properties of metal nanoparticles is also done. At the end of the chapter, the motivation of the work done is outlined. In chapter 2, the experimental set-ups for unpolarized and polarization resolved hyper-Rayleigh scattering (HRS) measurements at different wavelengths are described. Generation of IR wavelength of 1543 and 1907 nm using stimulated Raman scattering in gases have been presented in this chapter. In chapter 3, synthesis and characterization of copper nanoparticles are described. Four different size copper nanoparticles (5, 9, 25, and 55 nm) were prepared by laser ablation. Size dependencies of first hyperpolarizability were investigated at different wavelengths and it was found that β increases with increasing size of the particle and that the SHG originates mainly from the surface of the particle. Dispersion in first hyperpolarizabilities of the copper nanoparticles has also been investigated and we find that at incident and SH wavelengths far from the SPR absorption band, the hyperpolarizability is large compared to molecular hyperpolarizabilities. In chapter 4, the results of polarization resolved HRS measurements on copper nanoparticles of five different sizes at four different wavelengths (738, 1064, 1543 and 1907 nm) are reported. Polarization analyses show that at small particle size to wavelength (d/λ) ratio the dipolar contribution to SHG is dominant whereas the quadrupolar and retardation effects become important at larger d/λ values. The “small particle limit” in the SHG from coinage metal nanoparticles has been assessed based on our results on copper and others’ results on silver and gold nanoparticles. In chapter 5, the effect of surface capping on the first hyperpolarizability of copper nanoparticles is investigated. Polyvinyl pyrrolidone (PVP) has been used as a capping agent. The results obtained for bare and capped copper nanoparticles show that capping enhances the hyperpolarizability by a factor of 2. In the last chapter 6, general conclusions drawn on SHG from coinage metal nanoparticles based on this work are presented along with future perspectives.