Preliminaries -- Haar wavelets -- Solution of ordinary differential equations (ODEs) -- Stiff equations -- Integral equations -- Evolution equations -- Solving PDEs with the aid of two-dimensional Haar wavelets -- Fractional calculus -- Applying Haar wavelets in the optimal control theory -- Buckling of elastic beams -- Vibrations of cracked Euler-Bernoulli beams -- Free vibrations on non-uniform and axially functionally graded Euler-Bernoulli beams -- Vibrations of functionally graded Timoshenko beams -- Applying Haar wavelets in damage detection using machine learning methods.