This comprehensive review provides a rigorous, graduate-level synthesis of statistical methodologies essential for modern quantitative finance. We present a systematic framework spanning measure-theoretic probability, advanced statistical inference, financial time series analysis, volatility modeling, portfolio optimization, stochastic calculus, extreme value theory, Monte Carlo methods, high-dimensional statistics, and cutting-edge machine learning applications. Each topic is treated with mathematical depth, emphasizing both asymptotic theory and finite-sample implementation. The review covers classical approaches such as ARIMA-GARCH frameworks and factor models, alongside modern developments including random matrix theory for covariance estimation, sparse precision matrices via graphical LASSO, copula-based dependence modeling, and deep learning architectures for sequential data. Special attention is devoted to the unique challenges of financial data: heavy tails, volatility clustering, non-stationarity, microstructure noise, and the pervasive low signal-to-noise ratio. Advanced topics include Lévy processes, realized volatility estimators, high-frequency econometrics, Bayesian nonparametrics, causal machine learning, and reinforcement learning for trading. Model validation, multiple testing corrections, and robust inference are discussed throughout. This synthesis serves as both a pedagogical resource for doctoral students and a research compendium for practitioners, bridging the gap between statistical theory and quantitative finance practice.