The purpose of this book is twofold. We would like to offer our readers a collection of high quality papers in selected topics of Discrete Mathematics, and, at the same time, celebrate the 60th birthday of Jarik Nesetfil. Since our discipline has experienced an explosive growth during the last half century, it is impossible to cover all of its recent developments in one modest volume. Instead, we concentrate on six topics, those closest to Jarik's interests. We have invited leading experts and close friends of Jarik's to contribute to this endeavor, and the response has been overwhelmingly positive. We were fortunate to receive many outstanding contributions.