  As a low-energy effective model emerging in disparate fields throughout all
of physics, the ubiquitous $\varphi^4$-theory is one of the central models of
modern theoretical physics. Its topological defects, or kinks, describe stable,
particle-like excitations that play a central role in processes ranging from
cosmology to particle physics and condensed matter theory. In these lecture
notes, we introduce the description of kinks in $\varphi^4$-theory and the
various physical processes that govern their dynamics. The notes are aimed at
advanced undergraduate students, and emphasis is placed on stimulating
qualitative insight into the rich phenomenology encountered in kink dynamics.
The appendices contain more detailed derivations, and allow enquiring students
to also obtain a quantitative understanding. Topics covered include the
topological classification of stable solutions, kink collisions, the formation
of bions, resonant scattering of kinks, and kink-impurity interactions.
