The chapter discusses the model problem of boundary control for the wave equation, focusing on controlling the Dirichlet data of solutions. The problem involves finding a control function \( v \) on the lateral boundary \( \Sigma \) of a cylinder \( Q = \Omega \times [0, T] \) such that the solution \( u \) of the wave equation, subject to initial conditions \( u(0) = u_0 \) and \( u'(0) = u_1 \), satisfies \( u(T) = u'(T) = 0 \). The goal is to minimize the time \( T \) and the support \( \Sigma_0 \) of the control function \( v \). The Hilbert Uniqueness Method (HUM) by J.L. Lions is introduced as a systematic approach to this problem, which can be seen as an optimization problem to minimize the integral of \( v^2 \) over \( \Sigma \) under certain constraints. Exact boundary controllability is guaranteed for every pair \( (u_0, u_1) \) if a specific inequality holds for the solution \( \varphi \) of the wave equation with zero Dirichlet boundary conditions on \( \Sigma \). The minimal smoothness assumptions for the boundary \( \Gamma \) are discussed, noting that J.L. Lions' method requires \( \Gamma \) to be at least \( C^2 \), while C.Bardos-C.Liebeau-J.Rauch's method works for \( C^\infty \) boundaries but allows for optimal control with minimal support. The key condition for the inequality to be meaningful is that \( \frac{\partial \varphi}{\partial \nu} \in L^2(\Sigma_0) \).The chapter discusses the model problem of boundary control for the wave equation, focusing on controlling the Dirichlet data of solutions. The problem involves finding a control function \( v \) on the lateral boundary \( \Sigma \) of a cylinder \( Q = \Omega \times [0, T] \) such that the solution \( u \) of the wave equation, subject to initial conditions \( u(0) = u_0 \) and \( u'(0) = u_1 \), satisfies \( u(T) = u'(T) = 0 \). The goal is to minimize the time \( T \) and the support \( \Sigma_0 \) of the control function \( v \). The Hilbert Uniqueness Method (HUM) by J.L. Lions is introduced as a systematic approach to this problem, which can be seen as an optimization problem to minimize the integral of \( v^2 \) over \( \Sigma \) under certain constraints. Exact boundary controllability is guaranteed for every pair \( (u_0, u_1) \) if a specific inequality holds for the solution \( \varphi \) of the wave equation with zero Dirichlet boundary conditions on \( \Sigma \). The minimal smoothness assumptions for the boundary \( \Gamma \) are discussed, noting that J.L. Lions' method requires \( \Gamma \) to be at least \( C^2 \), while C.Bardos-C.Liebeau-J.Rauch's method works for \( C^\infty \) boundaries but allows for optimal control with minimal support. The key condition for the inequality to be meaningful is that \( \frac{\partial \varphi}{\partial \nu} \in L^2(\Sigma_0) \).