Explore quantum singular value transformation (QSVT) in this graduate-level lecture from the Park City Mathematics Institute's 2023 Program on Quantum Computation. Delve into the unification of quantum algorithms through a linear algebraic framework, starting with block encoding fundamentals. Learn essential polynomial approximation tools for applying QSVT and discover its applications in quantum algorithm design, particularly for data analysis, machine learning, and quantum simulation problems. Access accompanying lecture notes and problem sets to reinforce understanding of this cutting-edge framework that bridges quantum computing with classical linear algebra concepts.