A history should probably be started with an introduction. I, Peter Blöchl, studied Physics at the University of Karlsruhe, Germany, which is now the Karlsruhe Institute for Technology (KIT). For my PhD, I joined the group of Ole Krogh Andersen at the Max-Planck Institute for Solid State Research in Stuttgart, Germany. Ole Andersen was one of the world leaders in the field of first-principles calculations of the electronic structure of solids. Following a Post-doc with Sokrates Pantelides at the IBM Research center in Yorktown Heights in the US, I joined the group of Michele Parrinello at the IBM Zurich Research Laboratory in Rüschlikon, Switzerland. This is where I implemented the Projector Augmented Wave (PAW) method which is probably my contribution with the widest impact. While at IBM in Zurich, I prepared my Habilitation at the Vienna University of Technology in Austria. Finally, after 10 years in Rüschlikon, I wanted to build my own group and became University Professor for Theoretical Physics at Clausthal University of Technology in Germany.

These lecture notes, I started writing when I returned to academia in the year 2000 and began teaching the theoretical physics courses at Clausthal University of Technology and, later, at Göttingen University. The main goal was to insure the quality of my lectures by keeping track of good explanations, new ideas and by incorporating suggestions from the students.

One of the main messages from the lecture notes is that students can themselves understand and verify the foundation of our picture of the world down to the basic postulates and derivations. This is opposite to learning a collection of unrelated formulas and theories. While such a course can cover only a small part of our knowledge, it provides a set of basic tools and concepts, which can be combined and extended in various ways to tackle the mysteries of our world.

My approach also implies that these lecture notes are dynamical. The notes will change with every lecture that I give and with every round of proofreading. I am also using the notes in my daily work, and I revise the presentation and add or remove material. On the negative side of this approach is that the lectures may still contain mistakes, which is why they carry a big warning on the front page. It is not the best approach to simply copy equations out of the notes. Rather, one should verify the result oneself, by making use of the derivations, which are given in some detail.

The plan is that I develop these notes further during my active time and then leave this project together with its source files to the public.