Explore the fascinating world of topological phases in many-particle systems through this comprehensive lecture from the International Centre for Theoretical Sciences. Delve into the foundations of quantum condensed matter physics, examining electronic phases and their topological properties. Discover the Tenfold Way classification, understand the concept of topological insulators, and learn about their potential technological applications. Gain insights into cutting-edge research topics such as amorphous topological insulators and tunable topology. Suitable for graduate students and researchers in physics, this nearly two-hour talk covers essential quantum ideas, symmetries in fermionic systems, and the interplay between topology and ground states, providing a solid foundation for understanding the current state and future directions of research in topological phases of matter.