Fourth edition. Includes bibliographical references (pages 609-616) and index. Michael David Spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. He is the author of the five-volume Comprehensive Introduction to Differential Geometry. He received a Ph.D. from Princeton University under the supervision of John Milnor in 1964. "Without a clear and thorough understanding, students often find themselves stuck on repetitive problems without developing the critical thinking skills necessary for success in advanced courses and research. This gap in comprehension not only impacts academic performance but also slows progress in fields that rely on mathematical precision, such as engineering, physics, and computer science. Many standard textbooks focus on memorization rather than truly explaining the underlying theory, leaving learners unprepared for higher-level analysis and practical applications. 'Calculus' by Michael Spivak - 4th Edition offers the perfect solution for those wanting to move beyond rote techniques and achieve a deeper, more rigorous understanding of calculus."--Publisher's website. Prologue. Basic properties of numbers ; Numbers of various sorts -- Foundations. Functions ; Graphs ; Limits ; Continuous functions ; Three hard theorems ; Least upper bounds -- Derivatives and integrals. Derivatives ; Differentiation ; Significance of the derivative ; Inverse functions ; Integrals ; The fundamental theorem of calculus ; The trigonometric functions ; [pi] is irrational ; Planetary motion ; The logarithm and exponential functions ; Integration in elementary terms -- Infinite sequences and infinite series. Approximation by polynomial functions ; e is transcendental ; Infinite sequences ; Infinite series ; Uniform convergence and power series ; Complex numbers ; Complex functions ; Complex power series -- Epilogue. Fields ; Construction of real numbers ; Uniqueness of the real numbers.