This thesis presents a general framework for first-order temporal difference learning algorithms with an in-depth theoretical analysis. The main contribution of the thesis is the development and design of a family of first-order regularized temporal-difference (TD) algorithms using stochastic approximation and stochastic optimization. To scale up TD algorithms to large-scale problems, we use first-order optimization to explore regularized TD methods using linear value function approximation. Previous regularized TD methods often use matrix inversion, which requires cubic time and quadratic memory complexity. We propose two algorithms, sparse-Q and RO-TD, for on-policy and off-policy learning, respectively. These two algorithms exhibit linear computational complexity per-step, and their asymptotic convergence guarantee and error bound analysis are given using stochastic optimization and stochastic approximation. The second major contribution of the thesis is the establishment of a unified general framework for stochastic-gradient-based temporal-difference learning algorithms that use proximal gradient methods. The primal-dual saddle-point formulation is introduced, and state-of-the-art stochastic gradient solvers, such as mirror descent and extragradient are used to design several novel RL algorithms. Theoretical analysis is given, including regularization, acceleration analysis and finite-sample analysis, along with detailed empirical experiments to demonstrate the effectiveness of the proposed algorithms.