This chapter provides an introduction to topological solitons, focusing on the one-dimensional kink solution of the non-integrable $\phi^4$ model. The kink, a spatially localized non-perturbative configuration, is a fundamental example of topological solitons. The $\phi^4$ model, with its double-well potential, is widely studied in condensed matter physics, field theory, and cosmology. The chapter discusses the dynamical properties of kinks, including their scattering, radiation, and annihilation processes. In the non-integrable $\phi^4$ model, the collision of kinks and antikinks can lead to various outcomes, such as the formation of oscillating bound states or the bouncing and reflection of solitons. The author reviews the perturbative and non-perturbative aspects of the model, including the spectrum of perturbative fluctuations on the kink background. The mechanism of resonant bouncing scattering in $K\bar{K}$ collisions, where energy exchange between the kink's internal and translational modes plays a crucial role, is also discussed. Finally, the production of kink-antikink pairs in the collision of particle-like states, related to the resonance excitation of oscillon configurations, is explored. The chapter begins with the Lagrangian of the $\phi^4$ model and derives the classical kink solution, followed by an expansion in powers of the dimensionless parameter $\varepsilon$. The first-order corrections to the kink solution are obtained using the eigenfunctions of the operator $D^2$, which describe scalar field fluctuations on the kink background.This chapter provides an introduction to topological solitons, focusing on the one-dimensional kink solution of the non-integrable $\phi^4$ model. The kink, a spatially localized non-perturbative configuration, is a fundamental example of topological solitons. The $\phi^4$ model, with its double-well potential, is widely studied in condensed matter physics, field theory, and cosmology. The chapter discusses the dynamical properties of kinks, including their scattering, radiation, and annihilation processes. In the non-integrable $\phi^4$ model, the collision of kinks and antikinks can lead to various outcomes, such as the formation of oscillating bound states or the bouncing and reflection of solitons. The author reviews the perturbative and non-perturbative aspects of the model, including the spectrum of perturbative fluctuations on the kink background. The mechanism of resonant bouncing scattering in $K\bar{K}$ collisions, where energy exchange between the kink's internal and translational modes plays a crucial role, is also discussed. Finally, the production of kink-antikink pairs in the collision of particle-like states, related to the resonance excitation of oscillon configurations, is explored. The chapter begins with the Lagrangian of the $\phi^4$ model and derives the classical kink solution, followed by an expansion in powers of the dimensionless parameter $\varepsilon$. The first-order corrections to the kink solution are obtained using the eigenfunctions of the operator $D^2$, which describe scalar field fluctuations on the kink background.