A Foundation Course in Mathematics is based on a course on Foundations in one of the most famous and successful mathematics training programme titled Mathematics Training and Talent Search (MTTS) Programme which has been running in India since 1993. The book written in conversational style aims to impart a critical and analytical thinking which will be beneficial for students of any discipline. It also gives emphasis on problem solving and proof writing skills, key aspects of learning mathematics. The Subject matter of the book deals with logic, sets, functions and relations, the essential building blocks for higher mathematics. Numerous problems and exercises are chosen and interspersed inside the sections so that the student participates actively in the discussions. We believe that the study of this book will lay the foundation which will enable the readers to undertake courses in higher mathematics with confidence and due rigour, as has been seen from our experience.