This companion book is a valuable resource for all mathematics students who find their probability lecture daunting. For many students, this course is among the least popular and is perceived as particularly challenging. The present companion book enables students to better understand their lecture by focusing on clear explanations of the underlying concepts and ideas. It explicitly does not claim to be a complete textbook—there are already plenty of those. The rather abstract measure-theoretic concepts are not avoided, as is often the case in most elementary probability textbooks, but are explained in detail and illustrated effectively.