Book excerpt: This entertaining and serious book covers some key subjects, of number theory, algebra and analysis in the general theory of sixth-form and early-undergraduate mathematics. The reader-friendly style creates motivation to tackle more formal texts, ability to understand and enjoy mathematics, willingness to appreciate the proofs. Alice, Tweedledum, Twedledee and other L. Carroll?s characters make the book ingenious and pleasant. The main points in the exposition deal with logic, theorem proving, prime factorization, numbers and operations on them, equivalence relation, Euclid?s algorithm, induction, permutations, and transpositions, axioms for R, cardinality, sequences and series, convergence, graphs and continuity, selected exercises with hints and solutions, references with useful recommendations.--Reviewer: K.Peeva (Sofia).