This text provides a solid foundation in the basic logical concepts for most of the subjects encountered in university mathematics, including basic college-level algebra and analysis. The first edition has been completely rewritten and expanded in response to a decade of teaching the subjects. This text is written for the students beginning "abstract pure mathematics" at university or college level. For the student beginning to study mathematics at this level there is a distinction between what she or he has done in the past and what lies ahead. What the student needs to acquire mastery of what is virtually an entirely new language -the language of mathematics- and to adopt an entirely new way of thinking.