Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials monitoring of industrial processes enhancement of oil production by efficient reservoir characterization emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT) magnetic resonance imaging (MRI) positron emission tomography (PET) X-ray and ultrasound tomography etc. In the CIME Summer School on Imaging (Martina Franca Italy 2002) leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics.