This book provides an introduction to University maths courses and therefore bridges the gap between high-school and University-level maths. The style is less formal than in most text books and the book could be used as material for an introductory course (one semester) to analysis, or as preliminary reading material for the student who has opted for a science degree.
As may be gathered from the table of contents, the book starts with Sets, Functions and Relations, Proof by induction and reductio ad absurdum, Complex numbers, Vectors and Matrices and a short introduction to group theory. A grasp of such topics should facilitate the approach to delta-epsilon analysis and tackling the hard problems of continuity and limits. Exercises and problems are found throughout the book and the author has even provided additional exercises at the following web address: http://www.maths.bath.ac.uk/~masgcs/book1/. The book is written in a lively style and makes interesting reading for those who want to use it.
(translated from the Italian by Anna Beria).