Undergraduate courses in mathematics are commonly of two types. Onthe one hand are courses in subjects - such as linear algebra or realanalysis - with which it is considered that every student of mathematicsshould be acquainted. On the other hand are courses given by lecturersin their own areas of specialization, which are intended to serve as apreparation for research. But after taking courses of only these twotypes, students might not perceive the sometimes surprisinginterrelationships and analogies between different branches ofmathematics, and students who do not go on to become professionalmathematicians might never gain a clear understanding of the natureand extent of mathematics.

This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.

Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included.

The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.

This work on the foundations of Euclidean geometry aims to present the subject from the point of view of mathematics at the end of the 20th century, taking advantage of all the developments since the appearance of Hilbert's classic work. Here real affine space is characterized by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.