After its inception in the 1960s, dynamic nuclear polarization (DNP) became an important tool in the study of spin-dependent interactions in nuclear and elementary particle physics. But, except for the niche subject of magnetic ordering of nuclear spins, this remained its only application for many decades. The problem was that DNP requires the sample to be cooled to low temperature, while some of the most interesting potential applications---most notably the enhancement of sensitivity in magnetic resonance imaging (MRI)---require it to be at room temperature.

In 2003 a breakthrough was achieved by Aerdenkjaer-Larsen, Golman and co-workers. They polarized nuclear spins with DNP at liquid helium temperature, subsequently heated the sample rapidly to room temperature while dissolving it in water, and injected the fluid in an animal for MRI. This lead to a dramatic increase of more than four orders of magnitude of the sensitivity. Suddenly one could follow the injected substance in the animal and observe how and where it was metabolized. Within 10 years the first trial studies were already performed on human patients. This lead to a revival of DNP, not only for applications in MRI, but also to enhance the sensitivity of NMR in chemistry and biochemistry.

This development was a pleasant surprise for me, who after working on DNP from 1967 to 1991, switched to semiconductor physics, when the subject was declared nearly dead by the funding agencies. When I returned to DNP in 2005, I found the knowledge gathered in the 1960s and 1970s to be scattered over many papers, while the only book containing an overview is out of print. After giving a few courses at the Ecole Polytechnique Federale de Lausanne (EPFL) and the Paul Scherrer Institute (PSI) in Villigen, I was incited to write a monograph on the subject.

When embarking on such a project, one necessarily has to make choices. All major applications of DNP polarize nuclear spins in insulating, diamagnetic solids, and I decided to stick to DNP in such materials. The reader will therefore miss the Overhauser effect, despite recent indications that it might contribute to DNP in some insulators. I felt that this book certainly had to contain and explain the early knowledge gathered in the 1960s and 1970s and combine it into a coherent presentation. This inevitably meant that I had to skip a few more recent developments, in casu DNP in combination with magic angle spinning \cite{RosayGriffin,MentinkVigierVega} and combinations of pulsed NMR and ESR techniques in order to improve the efficiency of DNP. It also implied that no space was left to elaborate on applications.

The resulting book is aimed at researchers and students interested in DNP of nuclear spins in insulating solids. DNP in such solids is used in a wide range of fields, from bio-medicine to elementary particle physics, and an effort is made to render the material accessible to anyone with a working knowledge of the quantum mechanics of spin. In some cases this proved to be a daunting job. Some of the early work, in particular Provotorov's theory of magnetic resonance is theoretically demanding, even in the more accessible presentation by Abragam and Goldman. Fortunately, such theories can be substantially simplified if one accounts for the actual structure of the electron spin resonance (ESR) spectrum.

Background material is provided in two introductory chapters covering the statics and dynamics of a single spin 1/2---a two-level system. These chapters include a precise definition of polarization, relate it to other thermodynamic potentials, and derive its evolution in a magnetic field. Additional background is given in appendices. More material will be posted on my website www.wenckebach.net.

While pulsed magnetic resonance has taken over from continuous wave (CW) magnetic resonance many decades ago, DNP is still mainly a CW method and pulsed techniques for DNP are only in their infancy. To describe CW magnetic resonance, one constructs rate equations---i.e, sets of differential equations---for the evolution of the polarization of the electron and nuclear spins. Also the description of DNP is based on such rate equations. To pave the way for such an approach, Chapter 2 finishes with the derivation of a rate equation for a generalized two-level system.

Chapter 3 considers the various interactions of electron spins and nuclear spins in an insulating solid. The spin Hamiltonian is constructed and the ESR spectrum is derived. This chapter collects all elements needed to describe DNP, except electron spin-lattice interactions. Those are treated in Chapter \ref{chapter-5}.

Chapters 4 to 8 treat the various processes involved in DNP: saturation of the ESR signal by a CW micro\-wave field, spectral diffusion across the ESR signal, electron spin-lattice relaxation, polarization transfer from electron spins to nuclear spins by the solid effect, spatial diffusion of nuclear spin polarization, nuclear spin-lattice relaxation and thermal mixing. Each treatment starts with the fundamental transition of the process. Rate equations are derived for the evolution of the polarization of the one, two or three spins involved in this fundamental transition. Subsequently these rate equations are generalized to include more electron and nuclear spins.

Chapter 4 introduces CW ESR and treats saturation of ESR signals by a micro\-wave field: burning of a hole in the ESR signal and spectral diffusion widening the hole. Subsequently, this chapter derives the Provotorov equations describing the evolution of the ESR signal when spectral diffusion is fast. Next, Chapter 5 introduces lattice vibrations and adds electron spin-lattice relaxation to the Provotorov equations.

Chapter 6 is dedicated to the solid effect. It starts with the fundamental simultaneous transition of an electron spin and a nuclear spin induced by a CW microwave field. Next, it treats spatial diffusion of the polarization from nuclear spins near the electron spin to those further away. Finally, broadening of the ESR spectrum is included. When the ESR spectrum is narrow, this leads to the well-resolved solid effect. When the ESR line is broad and spectral diffusion is slow, DNP is governed by the differential solid effect. When spectral diffusion is fast, the solid effect leads to microwave induced thermal mixing. This case is, however, only of theoretical interest, as this mechanism is always superseded by the intrinsic thermal mixing treated in Chapter 8. Chapter 7 adds direct nuclear spin-lattice relaxation to the solid effect.

Chapter 8 introduces intrinsic thermal mixing induced by mutual interactions between electron spins. It starts with the fundamental triple spin transition involving two electron spins and a single nuclear spin. Next, broadening of the ESR spectrum and spatial diffusion of the nuclear spin polarization are added. It is demonstrated how this process provides a path for nuclear spin-lattice relaxation as well as a mechanism for DNP. To describe these processes, the Provotorov equations are further extended with thermal mixing. The cross-effect is introduced as a special case.

The last chapter is dedicated to some more recent developments on DNP. It treats fast polarization transfer, such that rate equations---as used to describe conventional DNP---cannot be justified anymore. The polarization transfer is then coherent---i.e. it is reversible. A new approach is introduced and applied to two pulsed techniques for DNP: nuclear orientation via electron spin locking (NOVEL) and the integrated solid effect (ISE).