Learning Abstract mathematics is a slow and complex process. This is partly because a student of mathematics must not only try to grasp the ideas and master the techniques of approaching mathematical problems, but she must also learn the language of mathematics. This is often a cause of unease for many students in their first serious mathematics course. The present text intends to help such students. It is designed to be used as a textbook in introductory abstract mathematics courses that are usually taken by beginning undergraduate students of mathematics as well as undergraduate and graduate students of natural sciences, engineering, and economics who plan to study more advanced subjects in abstract mathematics. It can also be used as a self-study book for any student with little or no prior experience with abstract mathematics. The only prerequisite is a basic knowledge of high school algebra and elementary arithmetic.