In this book the main subjects of naive set theory are introduced: functions, cardinalities, ordered and well-ordered sets, transfinite induction, ordinals and applications, e.g. on Hamel bases. The proofs are given in detail and with a high amount of motivation and illustration, e.g. in the discussion of the Cantor-Bernstein theorem and its applications. The proofs are accompanied by many problems (over 150), and the text is well understandable. The intention of the authors is to provide a leisurely exposition for a diversified audience, from undergraduate students to professional mathematicians who, e.g., want to “finally find out what transfinite induction is and why it is always replaced by Zorn’s lemma”. The first 40 pages deal with sets and their cardinals, and the next 70 pages with ordered sets, including well-founded sets and trees. A lot of applications are mentioned.