An adequate level of linguistic complexity in learning materials is believed to be of crucial importance for learning. The implication for school textbooks is that reading complexity should differ systematically between grade levels and between higher and lower tracks in line with what can be called the systematic complexification assumption. However, research has yet to test this hypothesis with a real-world sample of textbooks. In the present study, we used automatic measures from computational linguistic research to analyze 2,928 texts from geography textbooks from four publishers in Germany in terms of their reading demands. We measured a wide range of lexical, syntactic, morphological, and cohesion-related features and developed text classification models for predicting the grade level (Grades 5 to 10) and school track (academic vs. vocational) of the texts using these features. We also tested ten linguistic features that are considered to be particularly important for a reader's understanding. The results provided only partial support for systematic complexification. The text classification models showed accuracy rates that were clearly above chance but with considerable room for improvement. Furthermore, there were significant differences across grade levels and school tracks for some of the ten linguistic features. Finally, there were marked differences among publishers. The discussion outlines key components for a systematic research program on the causes and consequences of the lack of systematic complexification in reading materials.