This chapter discusses the solution methods for the single-variable problems. The methods involve fixed and variable bracketing methods such as interval search, Golden Section Search and Interval Halving Methods. In addition, the methods involving the evaluation of the gradient of the function referred to as Newton–Raphson method, secant method, bisection method and direct search methods have been elaborated on in very detail. It is important to mention that every method is explained with a detailed step-wise illustration revealing the nuances of every approach. It also helps in highlighting the distinctions among the methods. This chapter may lay a foundation for solving the complex non-linear problems involving several variables.