This first volume of the Third International Mathematics and Science Study (TIMSS) 1999 Video Study Technical Report focuses on every aspect of the planning, implementation, processing, analysis, and reporting of the mathematics components of the TIMSS 1999 Video Study. The report is intended to serve as a record of the actions and documentation of outcomes, to be used in interpreting the results and as a reference for future studies. The TIMSS 1999 Video Study is a complex and ambitious study conducted under the aegis of the International Association for the Evaluation of Educational Achievement (IEA) and managed by the U.S. Department of Education's National Center for Education Statistics in cooperation with its study partner, the National Science Foundation. Over a period of four years, the study researchers collected, transcribed, translated, coded, and analyzed hundreds of hours of videotapes of eighth-grade mathematics lessons in the seven participating countries. The design of the study built on the foundations established by the first TIMSS 1995 Video Study, but was improved and carried out through a collaborative process that involved individuals around the globe. Each of the chapters of this report, and the appendices, focuses on critical steps taken in the planning and implementation of the study, from its initial design to how the data was analyzed. One of the more complex tasks of the study was the development of a coding system that addressed critical questions and was applicable to each country's unique education system. The resulting coding system for the mathematics videos is discussed in detail in this report with the aim of making the system available for review, improvement, and possible application to future studies. Appended are: (1) TIMSS 1999 Video Study Transcription/Translation Manual; (2) Information Given to U.S. Superintendents, Principals, and Teachers; (3) U.S. Teacher and Parent Consent Forms; (4) TIMSS 1999 Video Study Data Collection Manual; (5) U.S. Mathematics Teacher Questionnaire; (6) U.S. Student Questionnaire; (7) TIMSS 1999 Video Study Mathematics Teacher Questionnaire Coding Manual; (8) Research Team in the TIMSS 1999 Video Study of Mathematics Teaching; (9) TIMSS 1999 Video Study Mathematics Video Coding Manual; and (10) Steps for Weighting the Data for Each Country. (Contains 56 tables, 10 figures and 17 footnotes.) [For "Third International Mathematics and Science Study 1999 Video Study Technical Report: Volume 2--Science. Technical Report. NCES 2011-049," see ED522248.]