This paper is the first of two articles (Part I and Part II) that presents the results of the new atomic mass evaluation, Ame2016. It includes complete information on the experimental input data (also including unused and rejected ones), as well as details on the evaluation procedures used to derive the tables of recommended values given in the second part. This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction, decay and mass-spectrometric results. These input values were entered in the least-squares adjustment for determining the best values for the atomic masses and their uncertainties. Details of the calculation and particularities of the Ame are then described. All accepted and rejected data, including outweighted ones, are presented in a tabular format and compared with the adjusted values obtained using the least-squares fit analysis. Differences with the previous Ame2012 evaluation are discussed and specific information is presented for several cases that may be of interest to Ame users. The second Ame2016 article gives a table with the recommended values of atomic masses, as well as tables and graphs of derived quantities, along with the list of references used in both the Ame2016 and the Nubase2016 evaluations (the first paper in this issue). Amdc: http://amdc.impcas.ac.cn/