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Using an experimental approach that combines high-resolution electron microscopy, electron diffraction and optical spectroscopies, including Raman scattering, Rayleigh spectroscopy and photoluminescence, on individual, spatially isolated and suspended (free-standing) single-walled (SWNTs) and double-walled carbon nanotubes (DWNTs), we have been able to investigate their phonons characteristics and optical properties. In this talk, we present an overview of the most significant results obtained via this approach. Particular attention is paid to the study of DWNTs, a coaxial composite of two SWNTs, which provide a unique model system for studying coupling at the nanoscale. We show how such coupling, originating from the van der Waals interaction between the inner and outer nanotubes, plays a crucial role in determining the characteristics of the collective radial breathing-like modes and G modes in DWNTs (for a review see Ref. 1-2). The effects of quantum interference between different electronic transitions on the experimental behavior of the G-modes intensity are discussed [3]. It must be emphasized that the theoretical predictions of Philippe Lambin and his collaborators have been invaluable in understanding a lot of these experimental data [4].