Mathematics is an inevitable subject and it has significant role in many real life problems. In order to formulate and solve many engineering problems, one has to relate the problems with various Mathematical concepts. A thorough understanding of mathematics is an essential one to do such problems easily. In this course, I would like to discuss some basic concepts of mathematics under the following titles.1. Real Analysis2. Complex analysis3. Vector analysisThis is a 10 week course comprising 40 modules, assignments and tests under the above mentioned topics.The course is helpful to those students they are doing BSc Mathematics degree course under various universities of India.This course will help students from science stream for the systematic study of the basic concepts of metric space, complex analysis and vector analysis. By completing this course, the students will have a legible understanding of basic concepts of metric space, complex analysis and vector analysis which will be useful in many situations.