These lecture notes are devoted to the obstacle problem \[ \begin{gathered} \int_\Omega|\nabla u(x)|^2 dx\to\min,\quad u\in K,\\ K= \{u\in H^1(\Omega)| u= \varphi\text{ on }\partial\Omega,\;u\geq \psi\text{ in }\Omega\}.\end{gathered}\tag{1} \] The notes are self-contained and give the basic results on regularity of solutions of (1), especially on the behavior of solutions near the boundary of the coincidence set.