This CS50x lecture provides a comprehensive overview of fundamental data structures in C, starting with the limitations of arrays and introducing dynamic memory allocation with `malloc` and `realloc`. It delves into abstract data types like queues (FIFO) and stacks (LIFO), then explores linked lists, binary search trees, hash tables, and tries, detailing their implementation, performance (Big O notation), and inherent time-space trade-offs. The lecture concludes by demonstrating how these abstract concepts manifest in real-world applications, emphasizing the critical role of choosing the right data structure for specific problems.