A general procedure for constructing Haar systems \(\mathcal H\) on any compact metrizable measurable space \((\Delta,\mu)\), hence on any compact region of the Euclidean space, is given. It is shown that a system \(\mathcal H\) has the desired properties, in particular, \(\mathcal H\) is complete and orthonormal in \(L^ 2_ \mu(\Delta)\), if the \({\mathcal H}\)-Fourier series of a function \(f\) converges uniformly when \(f\) is continuous on \(\Delta\) and converges in \(L^ p_ \mu\)-norm when \(f\in L^ p_ \mu(\Delta)\) for some \(1\leq p< \infty\). Sufficient conditions for uniqueness for \({\mathcal H}\)-series are obtained.