Gardiner (U. of Birmingham) writes for undergraduate and high school students, and general readers with some mathematical background. He explains why the calculus works, and emphasizes the critical need for precision when dealing with infinite mathematics. The 1982 edition was published by Springer-Verlag with the subtitle Background to Analysis , and is cited in Steen's Library Recommendations for Undergraduate Mathematics . Annotation (c) Book News, Inc., Portland, OR (booknews.com)