Ignition delay time, τ_ign, is a key quantity of interest that is used to assess the predictability of a chemical kinetic model. This dissertation explores the sensitivity of τ_ign to uncertainties in: 1. rate-rule kinetic rates parameters and 2. enthalpies and entropies of fuel and fuel radicals using global and local sensitivity approaches. We begin by considering variability in τ_ign to uncertainty in rate parameters. We consider a 30-dimensional stochastic germ in which each random variable is associated with one reaction class, and build a surrogate model for τ_ign using polynomial chaos expansions. The adaptive pseudo-spectral projection technique is used for this purpose. First-order and total-order sensitivity indices characterizing the dependence of τ_ign on uncertain inputs are estimated. Results indicate that τ_ign is mostly sensitive to variations in four dominant reaction classes. Next, we develop a thermodynamic class approach to study variability in τ_ign of n-butanol due to uncertainty in thermodynamic properties of species of interest, and to define associated uncertainty ranges. A global sensitivity analysis is performed, again using surrogates constructed using an adaptive pseudo-spectral method. Results indicate that the variability of τ_ign is dominated by uncertainties in the classes associated with peroxy and hydroperoxide radicals. We also perform a combined sensitivity analysis of uncertainty in kinetic rates and thermodynamic properties which revealed that uncertainties in thermodynamic properties can induce variabilities in ignition delay time that are as large as those associated with kinetic rate uncertainties. In the last part, we develop a tangent linear approximation (TLA) to estimate the sensitivity of τ_ign with respect to individual rate parameters and thermodynamic properties in detailed chemical mechanisms. Attention is focused on a gas mixture reacting under adiabatic, constant-volume conditions. The proposed approach is based on integrating the linearized system of equations governing the evolution of the partial derivatives of the state vector with respect to individual random variables, and a linearized approximation is developed to relate ignition delay sensitivity to scaled partial derivatives of temperature. The computations indicate that TLA leads to robust local sensitivity predictions at a computational cost that is order-of-magnitude smaller than that incurred by finite-difference approaches.