  The concept of synthetic dimensions in photonics has attracted rapidly
growing interest in the past few years. Among a variety of photonic systems,
the ring resonator system under dynamic modulation has been investigated in
depth both in theory and experiment, and has proven to be a powerful way to
build synthetic frequency dimensions. In this tutorial, we start with a
pedagogical introduction to the theoretical approaches in describing the
dynamically modulated ring resonator system, and then review experimental
methods in building such a system. Moreover, we discuss important physical
phenomena in synthetic dimensions, including nontrivial topological physics.
Our tutorial provides a pathway towards studying the dynamically modulated ring
resonator system, understanding synthetic dimensions in photonics, and
discusses future prospects for both fundamental research and practical
applications using synthetic dimensions.
