In this thesis, experimental studies are reported of ultrafast dynamics and third order optical nonlinear coefficients of carbon nanotubes, and time resolved coherent phonon dynamics of semiconductors and rare earth titanates. The thesis is divided into three parts. The first part presents (i) general introduction to theoretical background on nonlinear optical susceptibility and time resolved studies, and systems studied (chapter 1) and (ii) experimental techniques (chapter 2). The second part of the thesis deals with the measurements of third order nonlinear susceptibilities and ultrafast dynamics of single and double walled carbon nanotubes (chapter 3). The third part contains coherent phonon dynamics in semiconductors, Te (chapter 4), Bi2Te3 (chapter 5), and ZnTe (chapter 6) and spin-frustrated rare earth titanate insulators (chapter 7). Chapter 1: This chapter is a general introduction to the thesis. The chapter is divided into two parts: (i) light-matter interaction, and (ii) systems studied. Under light-matter interaction, we describe the required theoretical and conceptual background of nonlinear optical susceptibilities and time resolved carrier and phonon dynamics. In the next part, a brief summary of details of the systems studied, that include carbon nanotubes (single and double walled), semiconductors (Te, Bi2Te3 and ZnTe) and insulating spin-frustrated rare earth titanates (Gd2Ti2O7, Dy2Ti2O7 and Tb2Ti2O7), are presented. Chapter 2: Details of the ultrafast laser systems (femtosecond oscillator and amplifier), pulse width measurements and ultrafast experimental pump-probe and z-scan techniques, used in this thesis are given in this chapter. Chapter 3: Here the experimental results on the measurements of third order optical nonlinearity and ultrafast dynamics of single and double walled carbon nanotubes are presented. The chapter starts with a general overview of optical switching followed by known ultrafast dynamics and nonlinear studies on carbon nanotubes. In the next section, our theoretical modelling of nonlinear absorption and refraction in the limit of saturable absorption is described. The final two sections depict our results on single and double walled carbon nanotubes. These studies indicate that double walled carbon nanotubes are best candidates for ultrafast optical switching. Chapter 4: This chapter presents temperature and pump fluence dependent femtosecond time resolved reflectivity measurements on tellurium. The chapter starts with an overview of previous pump-probe reflectivity studies at room temperature on tellurium followed by our results. A totally symmetric A1 coherent phonon at 3.6 THz responsible for the oscillations in the reflectivity data is observed to be strongly positively chirped (i.e, phonon time period decreases at longer pump-probe delay times) with increasing photoexcited carrier density, more so at lower temperatures. We show for the first time that the temperature dependence of the coherent phonon frequency is anomalous (i.e, increasing with increasing temperature) at high photoexcited carrier density due to electron-phonon interaction. At the highest photoexcited carrier densities of ~ 1.4 x 1021cm-3 and the sample temperature of 3K, the lattice displacement of the coherent phonon mode is estimated to be as high as ~ 0.24 Å. Numerical simulations based on coupled effects of optical absorption and carrier diffusion reveal that the diffusion of carriers dominates the non-oscillatory electronic part of the time-resolved reflectivity. Finally, using the pump-probe experiments at low carrier density of 6 x 1018 cm-3, we separate the phonon anharmonicity to obtain the electron-phonon coupling contribution to the phonon frequency and linewidth. Chapter 5: This chapter begins with a introduction of previous ultrafast studies at room temperature on Bi2Te3 and then presents our results on the temperature dependent high pump fluence time resolved reflectivity measurements on Bi2Te3. The time resolved reflectivity data shows two coherently generated totally symmetric A1g modes at 1.85 THz and 3.6 THz at 296K which blue shift to 1.9 THz and 4.02 THz, respectively at 3K. At high photoexcited carrier density of ~ 1.7 x 1021cm-3, the phonon mode at 4.02 THz is two orders of magnitude higher positively chirped than the lower frequency mode at 1.9 THz. The chirp parameter, β is shown to vary inversely with temperature. The time evolution of these modes is studied using continuous wavelet transform of the time-resolved reflectivity data. The analysis shows that the build up time for the two coherent phonons is different. Chapter 6: This chapter starts with a general introduction on various as pects of ZnTe to be used in generation and detection of THz followed by our results on influence of carriers and sample temperature on coherent phonon and polariton generation in ZnTe. Combination of femtosecond Kerr, two photon absorption and impulsive stimulated Raman scattering experiments have been carried out to investigate the effect of pulse energy and crystal temperature on the generation of coherent polaritons and phonons in < 110 > cut ZnTe single crystals of three different resistivities. We demonstrate that the effect of two-photon induced free carriers on the creation of both the polaritons and phonons is largest at 4K where the free carrier lifetime is enhanced. Further, the temperature dependant impulsive stimulated Raman scattering on high and low purity ZnTe crystals allows us to unambiguously assign the phonon mode at 3.5 THz to the longitudinal acoustic mode at X-point in the Brillouin zone, LA(X) in contrast to the assignment as two-phonon process in earlier studies. Chapter 7: This chapter starts with an introduction on previous Raman studies on the pyrochlore systems accompanied by our results on the generation of coherent optical phonons in spin frustrated pyrochlore single crystals Dy2Ti2O7, Gd2Ti2O7 and Tb2Ti2O7 and their behavior as a function of sample temperature from 296K to 4K. At 4K, two coherent phonons are observed at 5.3 THz (5.0 THz) and ~ 9.3 THz (9.4 THz) for Dy2Ti2O7 (Gd2Ti2O7) whereas three coherent phonons are generated at ~ 4.8 THz, 8.6 THz and 9.6 THz for Tb2Ti2O7. In the case of spin-ice Dy2Ti2O7, a clear discontinuity is observed in the linewidths of both the coherent phonons as well as in the phase of low energy coherent phonon mode, indicating a subtle structural change as also suggested by Raman studies. In comparison, such changes are not seen in the coherent phonons of Gd2Ti2O7, and Tb2Ti2O7. Another important observation is the phase difference of ‘π’ between the modes in all the samples, thus suggesting that the driving forces behind the generation of these modes are different in nature unlike a purely impulsive or displacive mechanism. Chapter 8: This chapter summarizes our results reported in this thesis and gives future directions.