This textbook presents the theory of continuous-time and discrete-time signals and systems and shows how it can be used to solve analytically different problems. The book is dedicated to engineering students who are interested in mathematical methods used to solve real technical problems connected with signals and systems. The book covers, both in continuous- and in discrete domains, analysis of signals in time domain; orthogonal signal representation including Fourier series; convolution and correlation of signals; analysis of signals in the frequency domain and signal sampling, including aliasing and stroboscopic effects, among others. The author also emphasizes the role of Fourier-, one-sided Laplace- and one-sided Z transformations in signals and systems. Chosen methods of analog and digital filter design and stability criteria of analog and digital filters are also described. The author presents the necessary theory in the form of a concise "lecture" accompanied with a number of solved original problems. Every chapter ends with examples of complete solutions with explanation and necessary graphical visualization (graphs, schemes etc.).