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Network measurements are extremely important for the purpose of managing and configuring a network. They are also essential as part of controlled experiments for the purpose of designing new protocols and architectures. Consequently they are widely taken and used in current network operations and research. Unfortunately, most tools and most studies have been developed/conducted in a mostly ad hoc manner. Quite often, these tools and studies miss or make inefficient use of information contained within the measurements. Often this leads to poor quality, biased, and incorrect conclusions. Motivated by the above observations, we will argue in this talk for the need of a network measurement science that can deal in a principled way with the issues of measurement efficiency and measurement bias. To deal with measurement efficiency, we advocate the use of Fisher information during the design of measurement experiments and measurement tools. Briefly, Fisher information measures the amount of information that a single measurement provides to the computation of a statistic such as packet loss rate. We illustrate its application to the problem of estimating flow size distribution based on packet sampling, a widely used technique for performing network measurements. In the context of measurement bias, we shift our attention to measurements leading to the characterization of graphs as commonly found in the Internet and on-line social networks. We review several studies where biased measurements have led to flawed (but widely believed) conclusions and then describe how such biases can be easily avoided.