Geometry optimization is a fundamental step in the numerical modelling of chemical reactions. Many thermodynamic and kinetic properties are closely related to the structure of the reactant, product, and the transition states connecting them. Different from the reaction and product, which are local minima on the potential energy surface, a transition state is the first-order saddle point with only one negative curvature. Over years, many methods have been devised to tackle the problem. Locating stable structures is relatively easy with a reliable algorithm and high accuracy. One can follow the gradient descent direction to pursuit the local minimum until convergence is reached. But for the transition state, the determination is more challenging as either the up-hill or down-hill direction is allowed in the process. Motivated by the difficulty, many well-designed optimization algorithms are elaborated specifically to stress the problem. The performance of geometry optimization is affected by various aspects: the initial guess structure, the coordinate system representing the molecule, the accuracy of the initial Hessian matrix, the Hessian update schemes, and the step-size control of each iteration. In this thesis, we propose a new geometry optimization algorithm considering all the important components. More specifically, in Chapter 2, a new set of robust dihedral and redundant internal coordinates is introduced to effectively represent the molecular structures, as well as a computational efficient transformation method to generate a guess structure. In Chapter 3 and 5, a sophisticated robust algorithm is presented and tested to solve intricate transition state optimization problems. In Chapter 4, a new algorithm to exploring reaction pathways based on redundant internal coordinates is illustrated with real chemical reactions. Last but not least, in Chapter 6, a systematic test to explore the optimal methods in each procedure is presented. A well-performed combination of optimization methods is drawn for generic optimization purposes. All the methods and algorithms introduced in this thesis is included in our forth-coming open-source Python package named GOpt. It's a general-purpose library that can work in conjunction with major quantum chemistry software including Gaussian. More features are under development and await to be released in the coming update. / Thesis / Doctor of Science (PhD)