Class means a group of students meeting regularly to study a subject under the guidance of a teacher or a period during which a group of students meets for instruction.
example- today kelly is not going to attend the physics class.
Lesson is an assignment or exercise in which something is to be learned in classes.
example- this lesson is hard so you should pay attention more.
A course/coursebook or textbook, a book designed to accompany a specific academic course, or one specified by the writers of the course to be read by its students.
example- kelly is about to finish this chapter of English language coursebook.