This book has been growing during the last year exploiting many resources: my unfinished notes, recollecting material taught and not taught my time at the University of North Carolina at Charlotte, some of my online notes from these courses, some internet searches, some new ideas during writing,-to make it short out of an unfinished career that was unexpectedly interrupted by my eye problems. After being forced to retire about four years ago, I did continue to occupy myself with several topics from mathematics. Too, I finally took the time and effort to learn mathematics and use it to support my work. Because of the diversity and amount of topics, and to be able to present a book of handy size, I have divided the material into two volumes. The book in hand in just the first half, and the second half is to follow. Some material is much more concrete and computationally oriented than a math course at a university, other sections heavily depend on proofs worked out in all details, more carefully than possible in a short lecture. For most of the problems, but not all, solutions are included. In spite of all this, I want to remind the reader that this book cannot be read like a novel. The reader should not be disappointed while slowing down. Indeed paper and pencil at hand are advisable. Here is a paragraph by Hermann Weyl fitting nicely to the intention of the present book.