In mathematics, many first-year students are confronted with methods and ways of thinking for which they were not prepared in school. This book provides school leavers of varying qualifications with an easier entry into their studies. Initially, the work presents the necessary tools: axioms, logic, and set theory. The proof techniques learned are then applied to reintroduce topics familiar from school. Key areas include number systems, algebraic techniques, sequences and limits, functions, geometry and vector calculus, differentiation, integration, and complex numbers. The author places importance on clarity, despite the mathematical rigor. To deepen understanding, over 200 exercises are offered. The relaxed presentation, enriched with examples, historical insights, and anecdotes, transforms dry mathematics into an entertaining read.