Starting with an explanation of what 'proof' means to a mathematician, this student-friendly introductory text is aimed at undergraduates in mathematics and related disciplines. It shows students how to read and write mathematical proofs and describes how mathematicians investigate problems and formulate conjecture. Students develop their skills in logic by following precise rules, and examples and exercises relating to discovery and conjecture appear throughout. The author also covers mathematical concepts such as real and complex numbers, relations and functions and set theory.