This book is, more or less, the script of a lecture series entitled "Phase-Field Theory and Application," which I give at Ruhr University Bochum (RUB) in my department Scale-bridging Thermodynamic and Kinetic Simulation (STKS). It strongly rests on my personal experience during many years in academic and applied research with a special focus on "phase field." The idea is to combine a very brief presentation of the materials-related mechanisms alongside the theoretical background of the phasefield theory and, last but not least, to introduce numerical solutions. The lecture series is designed for graduate students and newcomers to phase-field theory. There are many aspects of phase field that will only be covered briefly in this script. At my university, we are continuing this lecture series with an advanced course in the format of a discussion seminar. We hope that we can continue with this in a second volume of the book. The 12-lecture course, as held at RUB, is condensed to seven lectures in this book.

An eighth lecture, "Quantum Phase Field," is added here that I do only in the advanced course: Just free your mind and enjoy! Exercises are recommended at the end of each lecture, and suggestions for further reading are given. Examples are added where appropriate. A short introduction to the phase-field code OpenPhase academic [1] is added as a "tutorial" with two examples as a beginning to your own research.