  Quantum algorithms offer significant speedups over their classical
counterparts for a variety of problems. The strongest arguments for this
advantage are borne by algorithms for quantum search, quantum phase estimation,
and Hamiltonian simulation, which appear as subroutines for large families of
composite quantum algorithms. A number of these quantum algorithms were
recently tied together by a novel technique known as the quantum singular value
transformation (QSVT), which enables one to perform a polynomial transformation
of the singular values of a linear operator embedded in a unitary matrix. In
the seminal GSLW'19 paper on QSVT [Gily\'en, Su, Low, and Wiebe, ACM STOC
2019], many algorithms are encompassed, including amplitude amplification,
methods for the quantum linear systems problem, and quantum simulation. Here,
we provide a pedagogical tutorial through these developments, first
illustrating how quantum signal processing may be generalized to the quantum
eigenvalue transform, from which QSVT naturally emerges. Paralleling GSLW'19,
we then employ QSVT to construct intuitive quantum algorithms for search, phase
estimation, and Hamiltonian simulation, and also showcase algorithms for the
eigenvalue threshold problem and matrix inversion. This overview illustrates
how QSVT is a single framework comprising the three major quantum algorithms,
thus suggesting a grand unification of quantum algorithms.
