Learn the fundamental implementation aspects of Density Functional Theory (DFT) in Quantum ESPRESSO through this comprehensive lecture by Dr. Ralph Gebauer from the 2017 ICTP workshop. Explore the core computational components including pseudopotentials (PPs), plane waves (PWs), Fast Fourier Transform (FFT) algorithms, and k-point sampling methods that form the foundation of electronic structure calculations. Gain deep insights into how these mathematical and computational techniques are integrated within the Quantum ESPRESSO software package to perform accurate first-principles calculations of materials properties. Understand the theoretical background and practical implementation details that enable efficient DFT calculations for studying electronic, structural, and optical properties of condensed matter systems.