This book is the first volume of a two-volume work on the Foundations of Quantum Mechanics, and is intended as a new edition of the author's book Die Grundlagen der Quantenmechanik  which was published in 1954. In this two-volume work we will seek to obtain an improved formulation of the interpretation of quantum mechanics based on experiments. The second volume will appear shortly. Since the publication of  there have been several attempts to develop a basis for quantum mechanics which is, in the large part, based upon the work of J. von Neumann . In particular, we mention the books ofG. W. Mackey , J. Jauch , C. Piron , M. Drieschner , and the original work ofS. P. Gudder , D. J. Foulis and C. H. Randall , and N. Zierler . Here we do not seek to compare these different formulations of the foundations of quantum mechanics. We refer interested readers to  for such comparisons.