This book builds up basic convex analysis and optimization together, using little beyond advanced calculus and very basic real analysis. Brief accounts of both are also included within the main text. The emphasis is on building a geometric intuition for the subject. This is aided further by figures. Two distinguishing features of the text are elementary alternative proofs of many results and an eclectic collection of useful facts from optimization and convexity often needed by researchers in optimization, game theory, control theory, mathematical economics, etc. In addition, there are pointers to more such results that are not covered here. A full chapter on optimization algorithms gives a bird's eye view of the field, touching upon many current themes. The book will be useful to students and researchers in the aforementioned fields, as also to the user community in various engineering disciplines..