Volume I Introduction: concepts from set theory. The integers 1.- Monoids and groups 2.- Rings 3.- Modules over a principal ideal domain 4.- Galois theory of equations 5.- Real polynomial equations and inequalities 6.- Metric vector spaces and the classical groups 7.- Algebras over a field 8.- Lattices and boolean algebras Volume 2 Introduction 1.- Categories 2.- Universal algebra 3.- Modules 4.- Basic structure theory of rings 5.- Classical representation theory of finite groups 6.- Elements of homological algebra with applications 7.- Commutative ideal theory: general theory and noetherian rings 8.- Field theory 9.- Valuation theory 10.- Dedekind domains 11.- Formally real fields