Wavelet theory provides a unified framework for various signal processing techniques, including multiresolution signal processing, subband coding, and wavelet series expansions. The Wavelet Transform (WT) is particularly useful for analyzing non-stationary signals, offering an alternative to the Short-Time Fourier Transform (STFT) by using short windows at high frequencies and long windows at low frequencies. This approach, known as "constant-Q" or constant relative bandwidth frequency analysis, allows for better time-frequency resolution. The WT can be seen as a decomposition of a signal onto a set of basis functions called wavelets, which are derived from a single prototype wavelet through dilations and contractions. The prototype wavelet acts as a bandpass filter, and the other wavelets are scaled versions of it. This introduces the concept of scale as an alternative to frequency, leading to a time-scale representation of the signal. There are several types of wavelet transforms, including the Continuous Wavelet Transform (CWT), Wavelet Series Expansion, and Discrete Wavelet Transform (DWT). The CWT provides a multiresolution analysis by varying the time and scale parameters, allowing for better time or frequency resolution depending on the signal's characteristics. The DWT, on the other hand, is used for discrete-time signals and is related to subband coding schemes in speech and image compression. The development of wavelet theory has been influenced by researchers from the "French school," including Morlet, Grossmann, and Meyer, who built strong mathematical foundations and named their work "Ondelettes" (Wavelets). Daubechies and Mallat further connected wavelet theory to discrete signal processing, leading to numerous theoretical and practical contributions. The paper aims to provide a review and tutorial on wavelet transforms, covering their main definitions, properties, and applications in signal processing. It emphasizes the importance of wavelets in analyzing non-stationary signals and discusses the trade-offs between time and frequency resolution. The paper also explores the connection between wavelet transforms and other signal processing techniques, such as spectrograms and scalograms, and introduces the concept of wavelet frames and orthonormal bases.Wavelet theory provides a unified framework for various signal processing techniques, including multiresolution signal processing, subband coding, and wavelet series expansions. The Wavelet Transform (WT) is particularly useful for analyzing non-stationary signals, offering an alternative to the Short-Time Fourier Transform (STFT) by using short windows at high frequencies and long windows at low frequencies. This approach, known as "constant-Q" or constant relative bandwidth frequency analysis, allows for better time-frequency resolution. The WT can be seen as a decomposition of a signal onto a set of basis functions called wavelets, which are derived from a single prototype wavelet through dilations and contractions. The prototype wavelet acts as a bandpass filter, and the other wavelets are scaled versions of it. This introduces the concept of scale as an alternative to frequency, leading to a time-scale representation of the signal. There are several types of wavelet transforms, including the Continuous Wavelet Transform (CWT), Wavelet Series Expansion, and Discrete Wavelet Transform (DWT). The CWT provides a multiresolution analysis by varying the time and scale parameters, allowing for better time or frequency resolution depending on the signal's characteristics. The DWT, on the other hand, is used for discrete-time signals and is related to subband coding schemes in speech and image compression. The development of wavelet theory has been influenced by researchers from the "French school," including Morlet, Grossmann, and Meyer, who built strong mathematical foundations and named their work "Ondelettes" (Wavelets). Daubechies and Mallat further connected wavelet theory to discrete signal processing, leading to numerous theoretical and practical contributions. The paper aims to provide a review and tutorial on wavelet transforms, covering their main definitions, properties, and applications in signal processing. It emphasizes the importance of wavelets in analyzing non-stationary signals and discusses the trade-offs between time and frequency resolution. The paper also explores the connection between wavelet transforms and other signal processing techniques, such as spectrograms and scalograms, and introduces the concept of wavelet frames and orthonormal bases.