English translation of Gauss' two memoirs which contain his final, definitive treatment of least squares and wealth of additional material.

These proceedings contain 25 papers, which are the peer-reviewed versions of presentations made at the 1st International Workshop on the Quality of Geodetic Observation and Monitoring (QuGOMS’11), held 13 April to 15 April 2011 in Garching, Germany. The papers were drawn from five sessions which reflected the following topic areas: (1) Uncertainty Modeling of Geodetic Data, (2) Theoretical Studies on Combination Strategies and Parameter Estimation, (3) Recursive State-Space Filtering, (4) Sensor Networks and Multi Sensor Systems in Engineering Geodesy, (5) Multi-Mission Approaches With View to Physical Processes in the Earth System.