The purpose of this book is to give a comprehensive introduction to the study of 2-metric spaces and linear 2-normed spaces. Since 1963, when S. Gaehler initially introduced the concepts of 2-metric spaces and linear 2-normed spaces, a number of authors have done considerable work on geometric structures of these spaces, for example, strict convexity, strict 2-convexity and uniform convexity, etc., and there are virtually no books concerning the theory of 2-metric spaces and linear 2-normed spaces. This book is introduced as a survey of the latest results on the relations between linear 2-normed spaces and normed linear spaces, completion of linear 2-normed spaces, 2-inner product spaces, strict convexity, strict 2-convexity, uniform convexity, isometry conditions, orthogonal relations and quadratic forms, etc. This compilation of results is intended as a reference work for scholars in the field and as an overview for those initiating research in this branch of mathematics.
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