Fixed point theory stands as a fundamental pillar in mathematics, offering powerful insights into the existence and properties of solutions across diverse mathematical spaces and equations. Originating from foundational work by Brouwer and Banach, fixed point theory has evolved into a versatile framework applicable in functional analysis, optimization theory, differential equations, and beyond. This review explores the breadth of applications of fixed point theory, emphasizing its role in proving the existence and uniqueness of solutions. Key concepts include the definition of fixed points in mappings f:X→X where X is a suitable space, and the conditions under which these fixed points exist. In functional analysis, fixed point theorems are pivotal in studying operators on Banach and Hilbert spaces, influencing the convergence of numerical methods and optimization algorithms. In differential equations, fixed point techniques provide crucial tools for establishing the stability and behavior of solutions over time. fixed point theory extends its impact beyond pure mathematics into fields such as economics, physics, and computer science, where problems often reduce to finding invariant solutions under specified transformations. By examining specific examples and methodologies, this review underscores the profound significance of fixed point theory in both theoretical advancements and practical applications across interdisciplinary domains.