Wavelet transform provides a powerful framework for analysing signals across multiple scales, addressing the key limitation of the Fourier transform, which lacks time localisation. Built upon the concepts of scalable and translatable mother wavelets, wavelet analysis enables simultaneous examination of temporal and frequency characteristics, making it well suited for non-stationary signals and images. This chapter introduces the foundations of continuous and discrete wavelet transforms, the construction of wavelet bases, multiresolution analysis, and the relationship between scaling and wavelet functions. It further explains how wavelet families such as Haar and Daubechies are formed and demonstrates two-dimensional wavelet decomposition for image processing, including practical applications in feature extraction and image compression.