Some Aspects of Complexity and Krylov Complexity

A review of the concept of Complexity as have emerged in studying long time properties of systems including blackholes will be presented. Some emphasis will be made on describing features of a particular form of Complexity, the Krylov Complexity. These include its features when interpolating among various types of systems: free, strongly integrable and chaotic ones. Finally I will present a case where we have shown that the value of the Krylov Complexity, a quantum information concept, is equal to the value of a geodesic in a certain background, a geometric concept.