Integral transform plays a vital role in the study of many applied engineering topics. Laplace transform and Fourier transform are basic tools to solve these problems. Fourier transform is only able to retrieve the global frequency content of a signal while the time information is lost. This book covers fundamental concepts of various integral transforms to understand and solve many applications in science and engineering. The book is suitable as a textbook for graduate, postgraduate students of applied science and engineering graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier transform, Laplace transform, Hankel transform, Mellin transform, wavelet, and Z - transforms with their simple problems to solve and apply to develop various biomedical life saving tools.