This chapter provides an overview of the applications of mathematics in various fields, including stochastic mechanics, random media, signal processing, image synthesis, mathematical economics, stochastic optimization, and finance. It highlights key texts and contributions in these areas, such as Wonham's "Linear Multivariable Control: A Geometric Approach," Hida's "Brownian Motion," and Protter's "Stochastic Integration and Differential Equations." The chapter also introduces a book on methods of mathematical finance by Ioannis Karatzas and Steven E. Shreve, which aims to bridge the gap between probability theory and financial applications. The book covers topics such as portfolio selection, derivative securities, and the role of financial institutions in facilitating capital flow. It emphasizes the importance of mathematical models in understanding and managing financial markets, and discusses the evolution of financial theory from the 1950s to the 1990s, including the work of Markowitz, Sharpe, Merton, and Black-Scholes. The chapter concludes with a preface and acknowledgments, detailing the authors' contributions and the support received during the writing process.This chapter provides an overview of the applications of mathematics in various fields, including stochastic mechanics, random media, signal processing, image synthesis, mathematical economics, stochastic optimization, and finance. It highlights key texts and contributions in these areas, such as Wonham's "Linear Multivariable Control: A Geometric Approach," Hida's "Brownian Motion," and Protter's "Stochastic Integration and Differential Equations." The chapter also introduces a book on methods of mathematical finance by Ioannis Karatzas and Steven E. Shreve, which aims to bridge the gap between probability theory and financial applications. The book covers topics such as portfolio selection, derivative securities, and the role of financial institutions in facilitating capital flow. It emphasizes the importance of mathematical models in understanding and managing financial markets, and discusses the evolution of financial theory from the 1950s to the 1990s, including the work of Markowitz, Sharpe, Merton, and Black-Scholes. The chapter concludes with a preface and acknowledgments, detailing the authors' contributions and the support received during the writing process.