We live in an information age, when computers and the software that drives them permeate every aspect of our society. There are two fundamentally important aspects of computation. - One concerns the resources needed to perform computational tasks: how many computational steps are needed, how much computer memory, etc. - The other concerns our ability to master the staggering complexity of the computer systems we create and use. The only way of managing this complexity is to use principles of modularity and abstraction, so that at each step of our design and construction of the system, we see only a very limited piece, whose complexity we can master. While the study of each of these aspects of computing has been greatly advanced as computer science has developed, currently we have a very limited understanding of how they relate to each other. Building on our previous work, this project aims to greatly enhance our common understanding of these issues, and to develop new mathematical tools and methods for studying computation based on this. This can lead in turn to new possibilities for fundamental advances in the field.