Explore fault tolerance in quantum computing through a comprehensive lecture on LDPC codes. Delve into the threshold theorem, surface codes, and the potential of high-rate low-density parity check codes to reduce overhead in quantum computers. Examine progress in code development, decoding algorithms, and fault-tolerant operations. Investigate hypergraph product codes, efficient decoding methods, and constant overhead fault tolerance. Compare the pros and cons of surface codes and high-rate LDPC codes, and consider open questions in the field. Gain insights from Daniel Gottesman of the Perimeter Institute in this Quantum Colloquium presented by the Simons Institute.