This report delves into the fundamental concepts of data structures and algorithms, providing a comprehensive understanding of their implementation and applications. It covers various sorting algorithms, including merge sort, heap sort, and linear search, with detailed explanations and pseudocode examples. The report also explores string operations, cryptography, and lexicological ordering, demonstrating practical applications of these concepts through Java code implementations. By analyzing time and space complexities, the report provides insights into the efficiency and effectiveness of different algorithms.