In this dissertation, the development and applications of a novel nonlinear multi-input-multi-output (MIMO) observer design technique based on trajectory linearization are presented, herein called the trajectory linearization observer (TLO). TLO complements the controller design method by trajectory linearization, known as trajectory linearization control (TLC). The nonlinear observer dynamics are first linearized along its nominal trajectory. The resulting MIMO linear time-varying (LTV) system is then transformed into the observer canonical form through a Lyapunov coordinate transformation. A differential algebraic parallel differential (PD) spectral assignment technique is employed to achieve locally exponential stability for the linearized LTV error dynamics. Major contributions of this work include: (i) The stability assessment and robustness analysis of the proposed TLO design method. The stability of the closed-loop linearized system with TLO is examined by virtue of the separation principle for LTV systems based on the PD-spectral theory. The stability of the closed-loop nonlinear system is then verified by linearizing the closed-loop system. (ii) High-gain observer theory is extended to time-varying systems using the PD-spectral theory, and is applied to the TLO design to alleviate the effects of modeling error. (iii) Existing results on LTV canonical forms are collected and presented in a unified manner. These results are not only fundamental to the canonical transformation and PD-spectral assignment, which are essential procedures for the proposed TLO design, but also significant to general studies on LTV systems and nonlinear systems. (iv) A case study is shown to compare the TLO method and the extended Kalman filter (EKF) method on stability, robustness and computational load. (v) Symbolic programs are developed for LTV canonical transformations and the calculation of observer gain. (vi) Nontrivial practical applications of the proposed TLO-TLC design method are developed to achieve output feedback tracking using MATLAB/SIMULINK simulation and real-time hardware-in-the-loop testing.