Construction of wavelets

Question

So far I've gone through the theory of construction of wavelets in finite dimensional case and also got a little bit idea on wavelets on the function space ($L^2(\mathbb R)$). It is clear that all the construction are interlinked. So in order to construct wavelets on $L^2(\mathbb R)$, where do we begin or how do we start. It'll be of great help if someone provide with some insight. Thanks in advance.