The author presents a theory whereby nets, terms and formulas represent concurrent process at three levels of abstractions: Petri nets are used to describe all details of the operational machine behavior of processes. Algebraic process terms such as Calculus of Communicating Systems (CCS) or Communicating Sequential Processes (CSP) two of the main models for parallel programming, are used to describe the architecture of processes, i.e. how they can be composed from subprocesses. Logical formulas of a first-order trace logic are used to describe the safety and liveness aspects of the communication behavior of processes as required by their users. The main emphasis and technical contribution of this theory are transformations for a top-down design of concurrent processes starting with formulas and proceeding through terms to nets.