This book makes it easier for beginners to get started with university mathematics and can help those undecided in choosing their field of study. It primarily presents detailed solutions to the exercises from the book "Mathematics for Beginners," but it also explains the mathematical background, placing great emphasis on motivations, thorough explanations, and examples. The book can be read independently or used as supplementary reading for any preparatory course or introductory book. It begins with an introduction to logic and set theory. Using the language acquired from this, mathematics from basic and advanced school courses is reformulated, including elementary algebra, limits, geometry, trigonometry, vector calculus, and differential and integral calculus. Proofs can be found in the referenced literature.