This chapter provides an introduction to convex analysis in finite-dimensional spaces, covering fundamental definitions, operations on sets, and key topological properties. It begins with basic notions such as convexity, affine and convex hulls, and vector subspaces. The chapter then explores the topological structure of convex sets, including relative interiors, closures, and separation theorems. Supporting hyperplanes and separation results play a crucial role in characterizing convex sets. Special attention is given to convex cones, polarity, and duality concepts. The chapter also discusses convex functions, their conjugates, and Fenchel duality, which plays a central role in optimization and variational analysis. These concepts form the foundation for more advanced topics in convex optimization.