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This review describes investigations into the localized surface plasmon resonance (LSPR) of silver nanoparticles from both experimental and theoretical perspectives. It is divided into two parts: 1) LSPR of silver nanoparticle arrays and its interaction with resonant adsorbates and 2) single-nanoparticle LSPR spectroscopy and sensing of two specific nanoparticle geometries: triangular nanoprisms and nanocubes. Part I addresses the problem of strong coupling between the plasmon resonance of the nanoparticle and the molecular electronic resonances of the adsorbates. In particular, it was shown that the shift in the LSPR wavelength induced by resonant adsorbates binding to nanoparticles is highly dependent upon the relative spectral position of the LSPR to the molecular resonance. This finding was applied to study the electronic structures of resonant adsorbates on metallic nanostructures. Furthermore, an optical nanosensor was designed to study low molecular weight substrate molecule interaction with cytochrome P450 proteins. Part II shows that the LSPR spectra of single nanoparticles are highly sensitive to all details of their geometry. These geometric details play an important role in determining the utility of a nanoparticle as a sensor. It was demonstrated that nanoprisms have a 1 nm per CH2 unit greater sensitivity to the binding of molecular adsorbates than truncated tetrahedral arrays despite being five times thinner, suggesting they will be excellent candidates for sensing large biomolecules. It was further shown, for the case of the nanocubes, that the energy of LSPR modes are not simply sensitive to their environments, but that the environment can actually affect the number of modes observed in a nanoparticle's LSPR spectrum. A figure of merit (FOM) has been defined for single-nanoparticle sensors, and the nanocubespsila high-energy peaks were shown to have the highest-value FOM measured to date.