Wavelets are mathematical tools used to represent signals such as audio files, pictures, videos, and various other types of data. The theory of wavelets has recently attracted attention in Mathematics because of potential in applications. At this point, the field of wavelet theory is fairly mature, and the literature contains a body of techniques which are exploited to design wavelets. One of these techniques relies on the construction of wavelet sets. A wavelet set is a set whose successive translations and dilations partition a line. In practice, wavelet sets are tricky to construct. In fact, there is no known classification of wavelet sets consisting of more than three intervals available in the literature. In the present thesis, we will provide a complete characterization of wavelet sets of four intervals. Additionally, we will present two algorithms which are used to construct wavelet sets of four intervals
