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Root-finding algorithms have been studied for ages for their various applications. Newton's Method is just one of these root-finding algorithms. This report discusses Newton's Method and aims to describe the procedures behind the method and to determine its capabilities in finding the zeros for various functions. The possible outcomes when using this method are also explained; whether the Newton function will converge to a root, diverge from the root, or enter a cycle. Modifications of the method and its applications are also described, showing the flexibility of the method for different situations.