The first part of the course is devoted to present some problems which can be classified as inverse problems. Examples supplied by mathematical models in mechanics, geophysics, medical imaging, heat and fluid diffusion are discussed. The common feature of these problems is their ill-posedness, according to the definition given by Hadamard. The attention is focussed on linear inverse problems expressed by integral equations of first kind. Methods for treating inverse problems and for restoring the well-posedness, such as the method of regularization, are treated.