This chapter introduces Rasch measurement theory (RMT) as a coherent, principled framework for constructing and interpreting measurement scales in the human sciences. Unlike the fragmented landscape of other psychometric models, RMT is grounded in the scientific ideals of invariance and specific objectivity. This enables comparisons that are independent of the specific items and persons involved. Five principles for invariant measurement are outlined with an emphasis on unidimensional scales, item-invariant person measurement, and person-invariant item calibration. The chapter reviews Rasch’s use of “ideal-type” models, connecting deterministic Guttman scaling with Rasch’s probabilistic approach, and demonstrates how variable maps visually represent persons and items along a latent continuum. The Dichotomous Model is presented as the foundational Rasch model, with an applied example from the Learning Stimulation Scale. This model illustrates how item and person locations determine the probability of correct responses that form the basis for evaluating invariant measurement. Extensions to the Dichotomous Model, including the Linear Logistic Rasch Model and Latent Regression Rasch Model are introduced within the broader statistical framework of Generalized Linear Mixed Models (GLMMs). These explanatory models incorporate covariates to link measurement with explanation, and this expands the range of RMT. The chapter concludes by situating RMT as both a measurement theory and a statistical modeling approach with broad implications for research and practice.