This paper explores the linguistic complexity of Greek textbooks as a readability classification task. We analyze textbook corpora for different school subjects and textbooks for Greek as a Second Language, covering a very wide spectrum of school age groups and proficiency levels. A broad range of quantifiable linguistic complexity features (lexical, morphological and syntactic) are extracted and calculated. Conducting experiments with different feature subsets, we show that the different linguistic dimensions contribute orthogonal information, each contributing towards the highest result achieved using all linguistic feature subsets. A readability classifier trained on this basis reaches a classification accuracy of 88.16% for the Greek as a Second Language corpus. To investigate the generalizability of the classification models, we also perform cross-corpus evaluations. We show that the model trained on the most varied text collection (for Greek as a school subject) generalizes best. In addition to advancing the state of the art for Greek readability analysis, the paper also contributes insights on the role of different feature sets and training setups for generalizable readability classification.