Using concepts like "table inheritance" (loosely) and join tables I would set things up in this manner:
Person
person_id, first_name, last_name, address
Student
student_id, person_id, matr_nr
Teacher
teacher_id, person_id, salary
Lecture
lecture_id, teacher_id, lect_name, lect_description, date
Attendees
lecture_id, student_id
Where Student and Teacher tables "inherit" from Person and the Attendees table is a Join table between Lecture and Student (teacher_id is used in the Lecture table to specify who's teaching the class. And by Join table best practice the table ought actually be named Lecture_Student or similar)
Alternate Design: (allows for multiple teachers of a class)
Person
person_id, first_name, last_name, address
Student
student_id, person_id, matr_nr
Teacher
teacher_id, person_id, salary
Lecture
lecture_id, lect_name, lect_description, date
Lecture_Student
lecture_id, student_id
Lecture_Teacher
lecture_id, teacher_id