A unique textbook devoted to introductory combinatorics, modeling and elementary number theory It is relatively simple to use in the classroom: 1 Chapter is designed for 2 weeks, and the notes can be provided designed for remote teaching or to display in the classroom Some of the advanced topics are good for research projects; the most popular ones in the author's classes were dimers, modeling tree growth, Magic squares and Pisano periods via finite fields Elementary number theory is exposed systematically (with complete proofs and good ones) An impressive collection of about 135 problems and 270 exercises (mostly with hints and answers) It contains a lot of history of mathematics and the games of chance, and many topics traditional in recreational mathematics The book also serves motivated high-school students, teachers of mathematics, and specialists in neighboring fields interested in combinatorics and its applications