Randomized algorithms, once used mainly in computational number theory, have now found widespread application due to their simplicity and speed. These algorithms use random numbers to influence their decisions, leading to varying performance across different executions. The analysis of such algorithms focuses on expected performance measures, ensuring they are valid for all inputs. The history of randomized algorithms dates back to Monte Carlo methods in numerical analysis and statistical physics. In complexity theory, the concept of a probabilistic Turing machine was introduced, leading to the development of concrete randomized algorithms by researchers like Berlekamp, Rabin, and Solovay. Rabin proposed randomization as an algorithmic tool, while Solovay and Strassen developed a randomized primality-testing algorithm. Various paradigms underlie randomized algorithms, including foiling an adversary, random sampling, abundance of witnesses, fingerprinting and hashing, random reordering, load balancing, rapidly mixing Markov chains, isolation and symmetry breaking, and probabilistic methods. These paradigms have led to efficient algorithms for diverse applications, such as primality testing, pattern matching, convex hull computation, and load balancing in communication networks. Randomized algorithms are particularly effective in scenarios where deterministic approaches are too slow or complex. They often provide probabilistic guarantees, ensuring high probability of correctness while maintaining efficiency. The book "Randomized Algorithms" by Motwani and Raghavan provides a comprehensive overview of these techniques. References to key works and authors are provided, highlighting the significant contributions to the field of randomized algorithms.Randomized algorithms, once used mainly in computational number theory, have now found widespread application due to their simplicity and speed. These algorithms use random numbers to influence their decisions, leading to varying performance across different executions. The analysis of such algorithms focuses on expected performance measures, ensuring they are valid for all inputs. The history of randomized algorithms dates back to Monte Carlo methods in numerical analysis and statistical physics. In complexity theory, the concept of a probabilistic Turing machine was introduced, leading to the development of concrete randomized algorithms by researchers like Berlekamp, Rabin, and Solovay. Rabin proposed randomization as an algorithmic tool, while Solovay and Strassen developed a randomized primality-testing algorithm. Various paradigms underlie randomized algorithms, including foiling an adversary, random sampling, abundance of witnesses, fingerprinting and hashing, random reordering, load balancing, rapidly mixing Markov chains, isolation and symmetry breaking, and probabilistic methods. These paradigms have led to efficient algorithms for diverse applications, such as primality testing, pattern matching, convex hull computation, and load balancing in communication networks. Randomized algorithms are particularly effective in scenarios where deterministic approaches are too slow or complex. They often provide probabilistic guarantees, ensuring high probability of correctness while maintaining efficiency. The book "Randomized Algorithms" by Motwani and Raghavan provides a comprehensive overview of these techniques. References to key works and authors are provided, highlighting the significant contributions to the field of randomized algorithms.