Precise measurements of ground deformation across the plate boundaries are crucial observations to evaluate the location of strain localization and to understand the pattern of strain accumulation at depth. Such information can be used to evaluate the possible location and magnitude of future earthquakes. Interferometric Synthetic Aperture Radar (InSAR) potentially can deliver small-scale (few mm/yr) ground displacement over long distances (hundreds of kilometers) across the plate boundaries and over continents. However, Given the ground displacement as our signal of interest, the InSAR observations of ground deformation are usually affected by several sources of systematic and random noises. In this dissertation I identify several sources of systematic and random noise, develop new methods to model and mitigate the systematic noise and to evaluate the uncertainty of the ground displacement measured with InSAR. I use the developed approach to characterize the tectonic deformation and evaluate the rate of strain accumulation along the Chaman fault system, the western boundary of the India with Eurasia tectonic plates. I evaluate the bias due to the topographic residuals in the InSAR range-change time-series and develope a new method to estimate the topographic residuals and mitigate the effect from the InSAR range-change time-series (Chapter 2). I develop a new method to evaluate the uncertainty of the InSAR velocity field due to the uncertainty of the satellite orbits (Chapter 3) and a new algorithm to automatically detect and correct the phase unwrapping errors in a dense network of interferograms (Chapter 4). I develop a new approach to evaluate the impact of systematic and stochastic components of the tropospheric delay on the InSAR displacement time-series and its uncertainty (Chapter 5). Using the new InSAR time-series approach developed in the previous chapters, I study the tectonic deformation across the western boundary of the India plate with Eurasia and evaluated the rate of strain accumulation along the Chaman fault system (Chapter 5). I also evaluate the co-seismic and post-seismic displacement of a moderate M5.5 earthquake on the Ghazaband fault (Chapter 6). The developed methods to mitigate the systematic noise from InSAR time-series, significantly improve the accuracy of the InSAR displacement time-series and velocity. The approaches to evaluate the effect of the stochastic components of noise in InSAR displacement time-series enable us to obtain the variance-covariance matrix of the InSAR displacement time-series and to express their uncertainties. The effect of the topographic residuals in the InSAR range-change time-series is proportional to the perpendicular baseline history of the set of SAR acquisitions. The proposed method for topographic residual correction, efficiently corrects the displacement time-series. Evaluation of the uncertainty of velocity due to the orbital errors shows that for modern SAR satellites with precise orbits such as TerraSAR-X and Sentinel-1, the uncertainty of 0.2 mm/yr per 100 km and for older satellites with less accurate orbits such as ERS and Envisat, the uncertainty of 1.5 and 0.5mm/yr per 100 km, respectively are achievable. However, the uncertainty due to the orbital errors depends on the orbital uncertainties, the number and time span of SAR acquisitions. Contribution of the tropospheric delay to the InSAR range-change time-series can be subdivided to systematic (seasonal delay) and stochastic components. The systematic component biases the displacement times-series and velocity field as a function of the acquisition time and the non-seasonal component significantly contributes to the InSAR uncertainty. Both components are spatially correlated and therefore the covariance of noise between pixels should be considered for evaluating the uncertainty due to the random tropospheric delay. The relative velocity uncertainty due to the random tropospheric delay depends on the scatter of the random tropospheric delay, and is inversely proportional to the number of acquisitions, and the total time span covered by the SAR acquisitions. InSAR observations across the Chaman fault system shows that relative motion between India and Eurasia in the western boundary is distributed among different faults. The InSAR velocity field indicates strain localization on the Chaman fault and Ghazaband fault with slip rates of ~8 and ~16 mm/yr, respectively. High rate of strain accumulation on the Ghazaband fault and lack of evidence for rupturing the fault during the 1935 Quetta earthquake indicates that enough strain has been accumulated for large (M>7) earthquake, which threatens Balochistan and the City of Quetta. Chaman fault from latitudes ~29.5 N to ~32.5 N is creeping with a maximum surface creep rate of 8 mm/yr, which indicates that Chaman fault is only partially locked and therefore moderate earthquakes (M