Matter wave interference is at the basis of quantum mechanics. After early experiments with electrons and neutrons, about 20 years ago atom interferometers were first realized. Since then, atom interferometry led to growing applications in basic and applied science. It has been used, for example, to measure gravity acceleration, rotations and fundamental physical quantities with unprecedented precision. Future applications range from tests of general relativity to the development of next generation inertial navigation systems. Several laboratories in the world are actively working in this field. The improving performances of atom interferometric apparatus also stimulated a deep understanding of the theory required to connect the measured interferometric phase shift to the physically relevant quantities.

The goal of the 2013 Varenna School on “Atom Interferometry” and of this volume, which is published about one year later, has been to cover the basic experimental and theoretical aspects and to provide an updated review of the current activities in the field, the main achievements, open issues and future prospects. Main topics include theoretical background and experimental schemes for atom interferometry, ultracold atoms and atom optics, comparison of atom, light, electron, neutron interferometers and applications, high precision measurements with atom interferometry and applications to tests of fundamental physics, gravitation, intertial measurements and geophysics, measurement of fundamental constants, interferometry with quantum degenerate gases, matter wave interferometry beyond classical limits, large area interferometers, atom interferometry on chips, interferometry with molecules. The School was organized as a series of minicourses, some seminar lectures on specific topics and poster presentations by the participants.

The large number of students attending the lectures, a demonstration of the interest and vitality of the field, was at the limit of the School capacity; everything ran smoothly thanks to the organization by Barbara Alzani and her team. Special thanks are due to the Scientific Secretary of the School, Dr. Fiodor Sorrentino. The inspiring atmosphere of Villa Monastero stimulated scientific discussions amongst the students and with the lecturers and likely new ideas that will lead to further advances of atom interferometry in the future.

This volume collects the notes carefully prepared by all the lecturers after the School with the assistance of Monica Bonetti (editorial office) and Marcella Missiroli (production office). We are confident that it will be a reference for students, newcomers and experts in the field of atom interferometry.

G.M. Tino and M.A. Kasevich