"How do you describe a matrix where the determinant of every submatrix is positive?" The answer to this simple question has a rich algebraic structure. The theory of Cluster Algebra was introduced in 2000 to study the above problem of "total positivity". This new theory quickly becomes one of the most important research areas in mathematics, which finds applications in representation theory, combinatorics, hyperbolic geometry, algebraic geometry, dynamical systems, quantum theory and mathematical physics. This is an introductory course for graduate and advanced undergraduate students. After treating carefully the basics, we will survey some of the research topics in cluster algebra, covering the required backgrounds, if necessary.