This course is designed as a basic introductory course in the analysis of metric spaces. It is aimed at providing the abstract analysis components for the degree course of a student majoring in mathematics. This course affords students an opportunity to gain some familiarity with the axiomatic method in analysis. The topics to be covered are: metric spaces, open spheres, open sets, limit points, closed sets, interior, closure, boundary of a set, sequences in metric spaces, subsequences, upper and lower limits of real sequences,  continuous functions on metric spaces, uniform continuity, isometry, homomorphism, complete metric spaces, compact sets in a metric space, Heine-Borel theorem, connected set, and the inter-mediate value theorem.