  We are interested in the spectral properties of the magnetic Schr\"odinger
operator $H_\varepsilon$ in a domain $\Omega \subset \mathbb{R}^2$ with compact
boundary and with magnetic field of intensity $\varepsilon^{-2}$. We impose
Dirichlet boundary conditions on $\partial\Omega$. Our main focus is the
existence and description of the so-called \textit{edge states}, namely
eigenfunctions for $H_{\varepsilon}$ whose mass is localized at scale
$\varepsilon$ along the boundary $\partial\Omega$. When the intensity of the
magnetic field is large (i.e. $\varepsilon <<1$), we show that such edge states
exist. Furthermore, we give a detailed description of their localization close
to the boundary $\partial\Omega$, as well as how their mass is distributed
along it. From this result, we also infer asymptotic formulas for the
eigenvalues of $H_\varepsilon$.
