This book is being published: M. Grandis Higher Dimensional Categories, From Double to Multiple Categories World Scientific Publishing Co., 2019 - Info at WS: https://www.worldscientific.com/worldscibooks/10.1142/11406 - Downloadable Introduction https://www.worldscientific.com/doi/pdf/10.1142/9789811205118_0001 ________ PREFACE The study of higher dimensional categories has mostly been developed in the globular form of 2-categories, n-categories, omega-categories and their weak versions. Here we study a different form: double categories, n-tuple categories and multiple categories, with their weak and lax versions. We want to show the advantages of this form for the theory of adjunctions and limits. Furthermore, this form is much simpler in higher dimension, starting with dimension three where weak 3-categories (also called tricategories) are already quite complicated, much more than weak or lax triple categories. This book can be used as a textbook for graduate and postgraduate studies, and as a basis for self-study and research. Notions are presented in a concrete way, with examples and exercises; the latter are endowed with a solution or suitable hints. Part I, devoted to double categories, starts at basic category theory and is kept at a relatively simple level. Part II can be used independently by a reader with some knowledge of 2-dimensional category theory. ________ The following exposition of my talk at CT2019, in Edinburgh, can also be viewed as a partial introduction to this book: "Adjunctions and limits for double and multiple categories" http://www.dima.unige.it/~grandis/CT%202019%20Edi.pdf ________ Regards, MG [For admin and other information see: http://www.mta.ca/~cat-dist/ ]