Abstract: The aim of this talk is to discuss multi-variable generalizations of one-dimensional wavelets, and to show that this subject leads to many interesting problems in algebraic number theory, topology and geometry. Since most of these problems require the use of non-analytical methods, this area may be appealing to a broader range of mathematicians, We start by describing how the question of the existence of the multi-variable Haar type wavelet, which is the simplest possible example of a compactly supported wavelet, leads to questions about the class numbers of certain extensions of the field of rational numbers. Next we consider the question of construction of smooth wavelet bases out of a higher dimensional multi-resolution analysis. This problem leads in turn to some topological questions about the existence of everywhere continuous tangent vector fields. Finally, the problem of the existence of Meyer type wavelets, leads to certain geometrical questions involving the action of expansive dilations in higher dimensional Euclidian spaces.