This book presents elements of wavelet theory. Wavelets' properties and their application to the prediction have been presented in synthetic and comprehensible way. One-dimensional and two-dimensional Haar wavelet and Daubechies wavelet have been described. Algorithm of Daubechies wavelet construction and wavelet transform with application to the non-complicated numerical example have been explicated in detail. In addition to a concise and comprehensive theoretical basis about wavelets, the book contains detail description of author's algorithm for time series prediction based on wavelet analysis and artificial neural networks. Author's algorithm has been described theoretically and mathematically, together with simulation in Matlab computer program. The book is intended for students, graduate students, researchers and all persons interested in issues of wavelets and their applications.