This　article　studies　the　problem　of　adaptive　boundary　observer　design　for　a　class　of　linear　hyperbolic　partial　differential　equations　(PDEs)　subject　to　in-domain　and　boundary　parameter　uncertainties.　Based　on　the　swapping　transformation　technique,　a　Luenberger-type　boundary　observer　with　the　least　squares　parameter　estimation　law　is　designed,　which　relies　only　on　the　measurements　at　boundaries　of　the　system.　By　employing　the　Lyapunov　function　method,　we　prove　that　the　exponential　convergence　of　the　proposed　boundary　observer　design　scheme　is　guaranteed　when　the　observer　gains　satisfy　a　set　of　matrix　inequality　conditions.　Finally,　we　illustrate　the　effectiveness　of　the　adaptive　estimation　scheme　by　applying　it　to　the　linearized　Aw-Rascle-Zhang　traffic　flow　model　involving　the　in-domain　relaxation　time　and　boundary　flux　fluctuation　uncertainties.