This undergraduate thesis explores the intricate world of sequential and parallel algorithms, which are fundamental to problem-solving and computational efficiency in computer science and information technology. The objective is to comprehensively analyze these algorithms, comparing their strengths, weaknesses, and real-world implications. The thesis sets out to answer critical questions such as the fundamental differences between sequential and parallel algorithms, circumstances where parallel algorithms excel, their performance in real-world scenarios, and associated trade-offs and challenges. Through empirical studies, benchmarking, and theoretical analysis, the aim is to shed light on the impact of algorithmic choice on computational efficiency. By delving into theoretical foundations, empirical investigations, and practical considerations, the thesis aims to equip future researchers and practitioners with insights into algorithm selection. Ultimately, the goal is to contribute to the ongoing discourse on computational efficiency, advancing the field of computer science and its applications.