Ion trapping initiated in Europe more than 50 years ago. Since then, both fundamental research and development of applications have been growing steadily, and a world-wide recognition was given with the Nobel prize in Physics earned by Wolfgang Paul and Hans Dehmelt in 1989 (see Paul W., Electromagnetic traps for charged and neutral particles, in Rev. Mod. Phys., 62 (1990) 531 and Dehmelt H., Experiments with an isolated subatomic particle at rest, in Rev. Mod. Phys., 62 (1990) 525). The last decades have seen a remarkable growth due, mainly, to the improvement of laser-based techniques for spectroscopy, cooling, and manipulation of ions. Nowadays ion trapping plays a crucial role in a wide range of applications, including atomic and plasma physics, chemistry, high-precision measurements, high-energy physics, and most recently the emerging field of quantum technologies, such as quantum information processing, quantum simulations, and quantum metrology. This is, perhaps, the research direction that in the last years experienced the most dramatic developments and exciting achievements, recognized by the Nobel prize in Physics to David Wineland (Wineland D. J., Nobel Lecture: Superposition, entanglement, and raising Schroedinger's cat, in Rev. Mod. Phys., 85 (2013) 1103), jointly awarded with Serge Haroche in 2012.

Trapping of charged particles requires a portfolio of theoretical and experimental competences, from the more fundamental physical issues to the technological details of the interactions between an ion and the electromagnetic radiation. Early-stage researchers typically have different backgrounds and receive various training and education. Nevertheless, they face quite similar theoretical questions and experimental challenges, which they often tackle with complementary approaches. The fundamental common tool has fostered the emergence of a larger community, who has realized that only a joint effort across the topical boundaries could further boost the field.

In 2013, for the first time in its history, the International School of Physics “Enrico Fermi” hosted a course completely devoted to ion trapping and designed to bring together and address the needs of this heterogenous population. One of the aims of the course was to exploit diversity and stimulate cross fertilization, by offering lectures and seminars on cutting-edge physics in all those fields where trapped ions play a prominent role, with some more emphasis on ion spectroscopy and manipulation. The lectures and reports contained in this volume partly review the wide range of subjects discussed along the course and provide, at the same time, an overview of the topical domain.

The book is opened with the lecture by Dietrich Leibfried and by David Lucas, which introduces the basic concepts and lays the foundations of ion trapping and laser manipulation of trapped particles. This contribution is meant to provide graduate students with the essential experimental toolbox and theoretical framework to perform spectroscopy with trapped ions. Building on this introduction, Shuichi Hasegawa's lecture reviews more specialized work on the creation and use of ion ensembles composed of various isotopes for physics and chemistry applications.

Clusters and crystals of ions in Paul traps are the subject of the lecture by Michael Drewsen, who provides an overview on their properties and applications. His lecture is followed by the theory lecture of Shmuel Fishman and coworkers, who show how a specific structural transition in ion crystals, the linear-to-zigzag transition, can be used as a testbed of fundamental models in statistical mechanics. The contributed paper by Tobias Burgermeister and Tanja Mehlstaubler then describes experiments which analyse the formation of structural defects of ion chains in Paul traps after performing parameter quenches across mechanical instabilities. Ion trapping and crystallization in multipole traps are reviewed in the lecture of Martina Knoop and collaborators, setting the focus on novel ion crystal structures and metrological applications. Ion clocks and frequency standards are the topics of Helen Margolis's lecture, which is accompanied by the contribution of Joseph Thom et al., developing a specific laser system for coherent manipulation of ions in microfabricated traps.

Quantum information processing and simulations with trapped ions were discussed in detail in a series of lectures which build on Leibfried and Lucas' contribution. This book contains several contributions on quantum technological applications, which were never previously reviewed in the school. Spectacular and most recent progress in the realization of quantum simulators with ion crystals is reviewed in Christopher Monroe's lecture. Jurgen Eschner's lecture gives a detailed account of the basic concepts and the remarkable advances in the control of single-ion/single-photon interactions, setting the basis for the realization of a quantum network whose nodes are trapped ions. A related progress report by a major Australian laboratory is presented in Ben Norton et al.'s contribution. Irene Marzoli's lecture focuses on the first proposed protocols for performing quantum computation with trapped electrons. The following report by Andreas Lemmer and collaborators discusses the performances of trapped-ion geometric phase gates for trapped ions in the presence of noise, whereas Humairah Bassa et al. show how to apply unsharp measurements to monitor the dynamics of single quantum systems.

Stefan Willitsch's lecture, and the participant contributions from Jyothi Saraladevi et al. and Henry Lopez et al. are placed at the end of this book, but at the forefront of this interdisciplinary research, and review the interaction of atoms and ions at the frontier between physics and chemistry. These investigations allow to gain insight at the very heart of chemical reactions, working at low temperatures and with an unprecedented control onto the experimental parameters.

We also mention the lecturers, who gave exciting courses but whose contributions are not contained in this book: Rainer Blatt delivered a series of lectures on quantum computation with trapped ions, starting from the basic building blocks till the most recent experimental realizations of quantum algorithms and error correction. Alex Retzker reviewed recent experimental observations and characterizations of kinks and solitons in ion crystals. Klaus Blaum reviewed the applications of ion trapping to nuclear physics and, in particular, to precision mass measurements of short-lived radioactive nuclides. Gerald Gabrielse presented and discussed the basic concepts, the latest advancements, and the challenges in trapping and manipulating single particles and antiparticles for high-precision measurements, determination of fundamental constants and tests of QED. Stefan Schlemmer reviewed experimental investigations of ion-molecule reactions which are of relevance for astrophysical studies. We finally mention Wolfgang Schleich, who gave a passionate and enlightening talk on Herbert Walther's seminal contribution to the development of the field of trapped ions.

Course 189 took place in 2013 from July 22nd to July 30th in the beautiful surroundings of Villa Monastero in Varenna on lake Como, and was inaugurated in presence of Luisa Cifarelli, president of the Italian Physical Society (SIF), on the special occasion of the 60th anniversary of the school. The spectacular location and the perfect organisation by the highly professional SIF staff, led by Barbara Alzani, have made Course 189 an extremely enjoyable, fruitful and successful event, fostering the interaction and stimulating the discussion between all participants. We are glad to acknowledge support by SIF and its Italian partners (Camera di Commercio di Lecco, Istituto Nazionale di Fisica Nucleare), as well as CNRS, Aix-Marseille Universite and TOPTICA Photonics AG. This School was organized in the frame of a wide collaboration network of ion trappers, financially supported by the COST framework. COST Action MP1001 “Ion Traps for Tomorrow's Applications” provided the largest part of funding, in particular for the young researchers.

We hope that the present volume, with its collection of selected topics and highlights, may serve as a useful reference and guidance to all the participants and as a source of inspiration for the next generation of scientists in ion trapping.

M. Knoop, I. Marzoli, G. Morigi