The Varenna summer school on Quantum Matter at Ultralow Temperatures featured important frontiers in the field of ultracold atoms. For the last 25 years, this field has undergone dramatic developments, which were chronicled by several Varenna summer schools, in 1991 on Laser Manipulation of Atoms, in 1998 on Bose-Einstein Condensation in Atomic Gases, and in 2006 on Ultra-cold Fermi Gases. The theme of the 2014 school demonstrates that the field has now branched out into many different directions, where the tools and precision of atomic physics are used to realise new quantum systems, or in other words, to quantum-engineer interesting Hamiltonians.

The topics of the school identify major new directions: Quantum gases with long range interactions, either due to strong magnetic dipole forces, due to Rydberg excitations, or, for polar molecules, due to electric dipole interactions; quantum gases in lower dimensions; quantum gases with disorder; atoms in optical lattices, now with single-site optical resolution; systems with non-trivial topological properties, e.g. with spin-orbit coupling or in artificial gauge fields; quantum impurity problems (Bose and Fermi polarons); quantum magnetism. Fermi gases with strong interactions, spinor Bose-Einstein condensates and coupled multi-component Bose gases or Bose-Fermi mixtures continue to be active areas. The current status of several of these areas is systematically summarised in this Volume.

The Varenna summer school attracted leaders in the field and students to spend nine days together in the beautiful surroundings of Lake Como. The unique spirit which can be traced back to Enrico Fermi and the unique atmosphere stimulated many scientific discussions about the current status and the future of the field. The many young active researchers, and the flurry of new ideas are a strong indication that in a few years time, it will be necessary again to review the new frontiers in ultracold atoms at a Varenna summer school.

On behalf of all the participants, we thank the Italian Physical Society and in particular Barbara Alzani, Ramona Brigatti and Marta Pigazzini for the perfect preparation and organization of a successful summer school, Monica Bonetti from the editorial office and Marcella Missiroli for editing the proceedings.

M. Inguscio, W. Ketterle, S. Stringari and G. Roati