The paper describes design of the FLUTE system, an intelligent tutoring system in the domain of formal languages and automata. The basic idea of the FLUTE system is a systematic introduction of students into the system's domain, in accordance with both the logical structure of the domain and individual background knowledge and learning capabilities of each student. Other intelligent tutoring systems in that domain are not described in the open literature. The knowledge in the FLUTE system is represented starting from ITS ontology that has been defined within a recently developed framework and a model of intelligent tutoring systems, called GET-BITS. A brief overview of the model/framework is also included. The contents that should be presented to the student during tutoring sessions are discussed and logical organization of such contents within the system is described. The system is analyzed in the paper from the pedagogical point of view. Every concept that a student has to learn during a session with FLUTE, the system illustrates by a number of examples. This makes the tutoring process more dynamic and facilitates learning.