This thesis presents a viewpoint for analyzing data-based systems using an operator-theoretic approach based on The Koopman, or composition, operator. The presented approach allows processes from measured systems to be studied in a linear setting even if the system of interest is nonlinear or ill-described. In this work we focus on numerical methods for problems emerging from building systems analysis; a setting where systems are high-dimensional and described by large data-sets (measured or simulation), but for which equations describing the system cannot be expressed analytically. In particular we present a variety of novel analysis techniques based on spectral properties of the Koopman operator that can be applied to a wide variety of applications ranging from the monitoring/visualization of spatially extended systems, model order reduction, and model calibration. Each chapter is dedicated to one specific application and the analytic tools developed for it. Numerous examples are presented to illustrates the capabilities of the framework.