This book is a supplementary resource intended to enhance the teaching and learning of a first-year university Calculus course. It can also be used in upper secondary school. It consists of selected paradoxes and sophisms that can be used as a pedagogical strategy by creating surprise and interest in the subject. In this book the following major topics from a typical single-variable calculus course are explored: Functions, Limits, Derivatives and Integrals. As with the author’s previous book “Counter-Examples in Calculus” (Maths Press, Auckland, New Zealand, 2004, ISBN 0-476-01215-5,116 p.) the intention of this book is to encourage teachers and students to use it in the teaching and learning of Calculus, with these purposes: • for deeper conceptual understanding • to reduce or eliminate common misconceptions • to advance one’s mathematical thinking, that is neither algorithmic nor procedural • to enhance generic critical thinking skills – analysing, justifying, verifying, checking, proving which can benefit students in other areas of life • to expand the ‘example set’ - a number of examples of interesting functions for better communication of ideas in mathematics and in practical applications • to make learning more emotional, active and creative The book can be useful for: • upper secondary school teachers and university lecturers as a teaching resource • upper secondary school and first-year university students as a learning resource